Analytical Study of Hydrodynamic Instability in the Flame: 2. Account of the Viscosity of the Gas in the Cold and Hot Areas

Hydrodynamic instability is examined with consideration given to the viscosity of the fresh gas and combustion products, as well as to the dependences of the flame speed on the front curvature and of the transport coefficients on the temperature. For the perturbation frequency, an approximate second-order dispersion equation is derived. The flame is completely stable at very high viscosity or small dimensions. The greatest destabilizing role of the thermal expansion coefficient manifests itself at its relatively small values. As the expansion coefficient increases, the viscosity of the gas in the flame zone increases rapidly. In addition, the stabilizing effect according to the Markstein model is enhanced by thermal expansion.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Effect of vorticity production on the structure and velocity of curved flames

A nonlinear equation describing curved stationary flames with arbitrary gas expansion theta = rho(fuel)/rho(burnt) is obtained in a closed form without an assumption of weak nonlinearity. The equation respects all conservation laws and takes into account vorticity production in the flame. In the scope of the asymptotic expansion for theta -->1, the new equation solves the problem of stationary flame propagation with accuracy of the sixth order in theta - 1. Its analytical solutions give the flame velocity in tubes of arbitrary width, which agrees with available results of direct numerical modeling.     

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.     

On the mechanism of the deflagration-to-detonation transition in a hydrogen-oxygen mixture

The flame acceleration and the physical mechanism underlying the deflagration-to-detonation transition (DDT) have been studied experimentally, theoretically, and using a two-dimensional gasdynamic model for a hydrogen-oxygen gas mixture by taking into account the chain chemical reaction kinetics for eight components. A flame accelerating in a tube is shown to generate shock waves that are formed directly at the flame front just before DDT occurred, producing a layer of compressed gas adjacent to the flame front. A mixture with a density higher than that of the initial gas enters the flame front, is heated, and enters into reaction. As a result, a high-amplitude pressure peak is formed at the flame front. An increase in pressure and density at the leading edge of the flame front accelerates the chemical reaction, causing amplification of the compression wave and an exponentially rapid growth of the pressure peak, which “drags” the flame behind. A high-amplitude compression wave produces a strong shock immediately ahead of the reaction zone, generating a detonation wave. The theory and numerical simulations of the flame acceleration and the new physical mechanism of DDT are in complete agreement with the experimentally observed flame acceleration, shock formation, and DDT in a hydrogen-oxygen gas mixture.     

On the equation of pulsating flame fronts in solid fuel combustion

A strongly nonlinear equation describing the dynamics of pulsations in solid fuel combustion is obtained. The method consists of extending the problem via introduction of an artificial parameter into boundary conditions leading to a separation of the spatial and the temporal scales within a low-frequency region. The interface dynamics equation obtained through an asymptotic expansion is then extrapolated toward the original values of parameters. The key point in the derivation is to restore the unexpected form of the principal nonlinearity generating a strongly dissipative region near a stagnation point of the front which is responsible for the stability of pulsations. The results of a numerical simulation of the equation demonstrate strongly relaxational stable oscillations of the flame front velocity.     

An Analytical Study of Hydrodynamic Instability in the Flame. 1. Viscous Gas in the Flame Zone

The problem of the hydrodynamic stability of slow combustion is analytically solved with consideration given to the viscosity of the gas in the flame zone, the temperature dependence of the viscosity, and the dependences of the flame speed on the front curvature according to the Markstein model and on the pressure. The viscous forces in the flame zone alone cannot ensure the stability of the flame at any values of the Reynolds number. These forces act only as amplifiers of the stabilizing factor according to the Markstein model or in the case of a negative dependence of the flame velocity on the pressure. This property of internal friction forces is the more pronounced, the stronger the viscosity increases with the temperature. Thermal expansion is not only a destabilizing factor, leading to an increase in viscosity and other transport coefficients, but also produces a stabilizing effect.     

Burning rate of homogeneous energetic materials with thermal expansion and varying thermal properties in the condensed phase

We present a study of the one-dimensional flame structure of combusting solid propellants that focuses on the effects of thermal expansion and variable thermal properties in the condensed phase. A nonlinear heat equation is derived for a burning thermo-elastic solid with temperature-dependent specific heat, thermal expansion, and thermal conductivity coefficients. It is solved for different modelling approximations both analytically and numerically. Explicit expressions are derived for the regression rate of the propellant surface as functions of surface temperature and thermal expansion parameters. A simple one-step reaction model of the gas phase is used to study the full structure of propellent flame and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance. Results are displayed for HMX and compared with experimental data and numerical simulation with fair success.     

A Study of premixed propagating flame vortex interaction

Experimental data is presented for the interaction between a propagating flame and a simple vortex flow field structure generated in the wake of solid obstacles. The interaction between gas movement and obstacles creates vortex shedding forming a simple flow field recirculation. The presence of the simple turbulent structure within the gas mixture curls the flame front increasing curvature and enhancing burning rate. A novel twin camera Particle Image Velocimetry, PIV, was employed to characterise the flow field recirculation and the interaction with the flame front. The technique allowed the quantification of the flame/vortex interaction. The twin camera technique provides data to define the spatial variation of both the velocity of the flow field and flame front. Experimentally obtained values of local flame displacement speed and flame stretch rate are presented for simple flame/vortex interactions.     

微重力环境下V型层流预混火焰锋面不稳定性分析

本章试图寻求描述火焰锋面动态特性的方法，以解释微重力环境下出现的V型火焰锋面的涟漪现象。采用线性稳定性理论从经典的G方程中导出了描述火焰锋面动态结构的一阶偏微分方程。采用该方程计算了声波扰动后，不同时刻的V型火焰锋面的动态结构．对于谐波扰动，其频率与波数的关系是分析固有火焰锋面不稳定性的基础。因此，微重力环境下V型火焰锋面的不稳定性可能是声波与谐波相耦合的结果。     

Consequence analysis of blast wave from accidental gas explosions

Recently, consequence analyses of accidental gas explosions are often carried out to assess the risk of chemical plants, hazardous-materials sites and new energy systems. In these consequence analyses, it is indispensable to adequately predict the blast-wave (pressure-wave) intensity from gas deflagrations. Some prediction models already exist; however, most of them are based on the theory for explosives and adjusting parameters are needed for evaluating gas deflagrations. In this study, new prediction methods for gas deflagrations were developed. From theoretical analysis of blast-wave generation by a gas deflagration, an evaluation equation of the blast-wave intensity was derived. As the scale of gas deflagration becomes larger, flame front instability (especially hydrodynamic instability) would be more effective and the flame propagating velocity starts to be accelerated. Therefore, the equation was modified considering the effect of flame instability. The evaluations by this modified equation agreed well with the results of large scale experiments. By this analysis, it was found that not only total energy release but also combustion reaction rate has to be introduced into the prediction of gas deflagrations. Using this concept, a modified scale model to predict the blast-wave intensity was developed by improving the previous scale model introducing the term of combustion reaction rate as burning velocity. Furthermore, scale analysis was performed to develop the new scaling law. The universal relationship between scaled distance and overpressure has been realized by this new scaling law for gas deflagrations. In summary, these results provide new methods for accurate prediction of the blast-wave intensity from gas deflagrations.     

Violent folding of a flame front in a flame-acoustic resonance

The first direct numerical simulations of violent flame folding because of the flame-acoustic resonance are performed. Flame propagates in a tube from an open end to a closed one. Acoustic amplitude becomes extremely large when the acoustic mode between the flame and the closed tube end comes in resonance with intrinsic flame oscillations. The acoustic oscillations produce an effective acceleration field at the flame front leading to a strong Rayleigh-Taylor instability during every second half period of the oscillations. The Rayleigh-Taylor instability makes the flame front strongly corrugated with elongated jets of heavy fuel mixture penetrating the burnt gas and even with pockets of unburned matter separated from the flame front.     

Autoignition-controlled flame initiation and flame stabilization in a reacting jet in crossflow

This paper describes an analysis of the mechanisms of autoignition-controlled flame initiation and flame stabilization in a nonpremixed jet in crossflows, using simultaneous high-speed (10 kHz) tomographic particle image velocimetry, OH-PLIF and line-of-sight flame emissions. Measurements are conducted on a turbulent, transverse, reacting propane jet issued into a crossflow generated by combustion of natural gas at an equivalence ratio of 0.4 with the crossflow velocity of 10 m/s, the crossflow temperature of 1350 K and the jet momentum flux ratio of 41. While several prior studies have analyzed the lifted character of the flame in similar configurations, we show that several dynamic processes precede the leading edge of the lifted diffusion flame, including formation and evolution of “autoignition kernels”, “flame kernels” and “flame fragments”. “Autoignition kernels”, i.e., discrete compact reaction zones with the peak hydroxyl (OH) fluorescence intensity below that of the diffusion flame, initiate preferably at bulges along the jet periphery where the strain rates and the scalar dissipation rates are lower. The autoignition kernel grows in both size and the OH-fluorescence intensity as it convects downstream. An autoignition kernel transitions into a propagating flame kernel, which quickly gets distorted and elongated in the direction of the principal expansion strain rate to form a flame fragment. Neighboring flame fragments merge with each other and with the downstream diffusion flame via edge-flame propagation. Merging of upstream flame fragments with the downstream diffusion flame results in an upstream advancement of the diffusion-flame front. The diffusion flame front is intrinsically unsteady because of the rather random formation and evolution of autoignition kernels, flame kernels and flame fragments, presumably due to the stochastic velocity, the strain rate and mixture-fraction oscillations.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

The unstable behavior of cellular premixed flames induced by intrinsic instability

The unstable behavior of cellular premixed flames induced by intrinsic instability is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier–Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through the flame front; the diffusive-thermal effect is caused by the preferential diffusion of mass versus heat. A disturbance with several wavelength components is superimposed on a planar flame, and the formation of a cellular flame induced by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the combination and division of cells are observed. The behavior of cellular-flame fronts becomes more unstable when the Lewis number is lower than unity, since the diffusive-thermal effect has a great influence on the unstable behavior. The cell size changes with time, and its average is greater than the critical wavelength and becomes smaller by decreasing the Lewis number. The flame velocity of cellular flames depends strongly on the length of computational domain in the direction tangential to the flame front. As the length of computational domain increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances play an important role in the shape of cellular flames, i.e., in the flame-surface area.     

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.     

Experimental investigation on the flame front resistance of gas channel growth with melt formation in iron ore sinter beds

The resistance of the flame front within the solid bed constitutes a fundamental and crucial area in porous bed combustion as the flame front propagation is highly related to the productivity and product quality. This paper focuses on the iron ore sintering, a thermal agglomeration process in steel mills. The results from a detailed experimental study of the pilot-scale pot tests under the conditions of a wide range of fuel rate are presented. The primary objective is to provide better understanding of the growth of gas channels relating to melt formation in the flame front and its resistance to flow. The sintering bed was divided into several zones based on the temperature profile and component distribution. Even though there is a continuous one-to-one replacement of humidified zone with porous sintered zone, a constant air flow rate during sintering could be obtained, indicating the ～100?mm high-temperature zone has a controlling effect on sintering bed permeability. The specific pressure drop value in high-temperature zone increases from ～3?kPa in upper bed to ～7?kPa in bottom bed, which varies with the bed temperature and structure properties. Both the green bed and sintered bed were scanned by X-ray computed tomography, the reconstruction and image analysis showed that the sintered bed has large gas channels and many more closed pores due to solid-melt-gas coalescence. More melt is generated when the heat is accumulated along the bed or input higher coke content, showing a propensity to suppress the gas channel growth and amplify the mismatch of gas transportation along the bed. Higher coke rate leads to a higher resistance in flame front, resulting in a slower flame front speed. These results are aimed to provide quantitative validation for improvements of a numerical sintering model in a future work.