Influence of distributed solid-phase reactions on deflagrations in confined porous propellants

Combustion processes in energetic materials are often modeled by a surface gasification reaction followed by a distributed gaseous flame. However, under confinement, deflagrations in porous or granular propellants are generally accompanied by an increasing pressure difference, or overpressure, between the burned-gas region and the unburned reactants deep within the pores of the material. As the overpressure and/or the solid-phase reaction rate become sufficiently large, the gaseous and solid reaction zones tend to merge into a single multiphase reaction region. Furthermore, in certain parameter regimes, the gas flame penetrates into the porous solid, resulting in subsurface gaseous combustion. When the activation energies of the gaseous and solid-phase reactions are of the same order of magnitude and/or the overpressure becomes significant, gasification reactions may also become active within the solid, thus eliminating a distinct propellant surface and forming a distributed multiphase reaction layer. A large activation-energy analysis of this scenario is presented to study the effects of distributed solid reactions on the deflagration structure and the burning-rate response. The burning-rate eigenvalue is obtained from a numerical solution of the reaction-zone problem, and the results are calculated for various overpressures as well as different gas-to-solid activation-energy and thermal conductivity ratios. It is observed that increasing overpressure results in a more spatially distributed solid-phase reaction and a rapidly increasing flame-propagation speed.     

Theory of the transition from conductive to convective burning

The experimentally known phenomenon of an abrupt transition from slow conductive to fast convective (penetrative) burning in a confined gas-permeable explosive is discussed. A simple model, involving only the most essential physical ingredients, is formulated and analyzed. A good qualitative agreement between theoretical and experimental dependencies is obtained. The transition is triggered by a localized autoignition in the extended resistance-induced preheat zone formed ahead of the advancing deflagration, provided the pressure difference between hot gas products and gases deep inside the pores of the unburned solid exceeds a certain critical level. In line with observations the critical overpressure increases with diminishing permeability.     

Curvilinear deflagration of energetic materials

The effects of material interface curvature on deflagration of a homogeneous solid energetic material (EM) is studied in a limit when the radius of curvature is much larger than the deflagration front thickness. Under the assumption of quasi-steady burning, a method of matched asymptotics is employed do derive first-order curvature corrections to the mass flux across the gas–solid interface as well as to the interface temperature. As an illustration, a problem of quasi-steady spherical particle deflagration is solved numerically and the simulation results are used to verify those obtained through asymptotic analysis. An algorithm for a fully-coupled unsteady solver suitable for EM deflagration simulation is presented. Numerical solution of the unsteady spherical particle deflagration is used to show that the assumption of quasi-steady deflagration is valid.     

Modelling of the transition from conductive to convective burning in porous energetic materials

This paper is concerned with a theoretical interpretation of an abrupt shift from the slow conductive to fast convective burning observed in the combustion of gas-permeable explosives under gradual elevation of the ambient pressure. The paper is a revision of our recent communication on the problem, and is based on the amended heat equation, which meets the requirement of the conservation of energy lacking in the previous model. It appears, however, that both formulations lead (in appropriately chosen units) to a largely similar picture of the transition. The transition is triggered by a localised autoignition in the extended resistance-induced preheat zone formed ahead of the advancing deflagration, provided the pressure difference between hot gas products and gases deep inside the pores of the unburned solid exceed a certain critical level. For moderately high activation energies the critical overpressures are comparable to those observed experimentally. In line with observations, the critical overpressure increases with diminishing permeability. The amended formulation implies the possibility of overpressure-driven gasification waves occurring even in the absence of chemical heat release.     

Flame spread across surfaces of PBX 9501

There is little flame spread data for homogeneous energetic materials and no data for nitramines. We report the results of flame spread experiments of PBX 9501 (HMX (cyclotetramethylenetetranitramine) based explosive). The horizontal flame spread rate, S_f, is of the same order of magnitude as normal deflagration and varies nearly as the square root of pressure, as our scaling analysis presented here predicts. In the vertical orientation, the flame propagation downward was observed to be slightly faster than horizontal flame spread, presumably because of the melt layer flowing downward on the sample. In an accident scenario, a charge may be fractured or the surface roughened. Consequently, we also examined the effect of roughness. Minor roughness created by explosives machining was found to have a negligible affect on flame spread. However, more significant roughness can increase the rate between two and three times over normal flame spread for the conditions considered here. In addition we examine the effect of sample edges and configuration. Corners result in more favorable heat loss and therefore affect flame spread rate. We argue that the increased spread rate on edges and rough surfaces is because of favorable heat transfer convergence.     

Modelling of candle burning with a self-trimmed wick

As an example of a coupled gas-phase diffusion flame with porous media flow, a candle burning model with a porous wick is offered in this paper. The porous media analysis includes capillarity-induced liquid flow, liquid vaporisation, vapour motion and re-condensation and multi-phase heat transfer. Coupling with the gas phase flame is through the conservation of mass, momentum and energy at the wick surface. The steady state solutions obtained not only yield the flame structure but also the detailed flow pattern and saturation distributions inside the wick. One of the novel features of the present model is the capability to address the self-trimming phenomena of candle burning. The self-trimming wick length and the associated flame characteristics have been computed as a function of gravity level, wick permeability and wick diameter.     

Modeling of HMX combustion

A mechanism of HMX combustion was proposed and the corresponding model was developed under the assumption that the combustion wave consists of two zones, with consideration given to the reaction of decomposition and vaporization of the initial energetic material in the condensed phase and the subsequent decomposition of its vapor in the gas phase. An analysis of the results showed that, at low pressures, the burning rate is largely determined by the exothermic decomposition of the material in the condensed phase, but at pressure above ∼20 atm, the processes in the gas phase begin to play an increasingly important role, where the limiting process is the bimolecular activation reaction with the subsequent dissociation of HMX accompanied by the secondary reactions between the products. A comparison of the calculation results with experimental data showed that the model adequately describes a number of characteristics of the combustion wave and ballistic properties, such as the burning rate and its sensitivity to pressure and initial temperature.     

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.     

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.     

Analysis of ignition of a porous energetic material

A theory of ignition is presented to analyse the effect of porosity on the time to ignition of a semi-infinite porous energetic solid subjected to a constant energy flux. An asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. As in the classical study of a nonporous solid, the transition stage consists of three spatial regions in the limit of large activation energy: a thin reactive–diffusive layer adjacent to the exposed surface of the material where chemical effects are first felt, a somewhat thicker transient–diffusive zone and, finally, an inert region where the temperature field is still governed solely by conductive heat transfer. Solutions in each region are constructed at each order with respect to the density-ratio parameter and matched to one another using asymptotic matching principles. It is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the nonporous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gaseous phases. A positive correction to the leading-order ignition-delay time, however, is provided by the convective flow of gas out of the solid, which stems from the effects of thermal expansion and removes energy from the system. The latter phenomenon is absent from the corresponding calculation for the nonporous problem and produces a number of modifications at the next order in the analysis arising from the relative transport effects associated with the gas flow.     

A flame technique to isolate the detonation/product interface relevant to rotating detonation engines

A novel experimental technique is proposed to study the detonation propagation in a layer of non-reacted gas weakly confined by combustion products. This problem is relevant to rotating detonation engines, where transverse detonations are confined by products of a previous rotation cycle, and other applications such as industrial safety. The experimental technique utilizes a flame ignited along the top wall in a long channel. The preferential growth of the flame along the long direction of the channel creates a finger flame and permits to create a narrow layer of unburned gas. A detonation ignited outside of this layer then propagates through the layer. This permits to conduct accurate observations of the detonation interaction with the inert gas and determine the boundary condition of the interaction. The present paper provides a proof-of-concept demonstration of the technique in a 3.4 m by 0.2 m channel, in which long finger flames were observed in ethylene-oxygen mixtures. The flame is visualized by high-speed direct luminosity over its entire travel, coupled with pressure measurements. A direct simulation of the flame growth served to supplement the experiments and evaluate the role of the induced flow by the flame growth, which gives rise to a non-uniform velocity distribution along the channel length. Detonation experiments were also performed at various layer heights in order to establish the details of the interaction. The structure was visualized using high speed Schlieren video. It was found that an inert shock always runs ahead of the detonation wave, which gives rise to a unique double shock reflection interaction.     

Effect of unsteady pressure rise on flame propagation and near-cold-wall ignition

Thermodynamic pressure rise during combustion is a key feature in internal combustion engines. Yet, hardly any studies have been conducted to investigate the effects of transient pressure rise on flame propagation as well as on the ignition of the unburned gas. In this study, the effects of unsteady pressure rise were parametrically studied using a one-dimensional reacting flow model in which the thermodynamic pressure variation is an independent variable and thus its rate of rise can be controlled. It was determined that large rates of pressure rise can significantly increase the mass burning flux of a laminar flame and that this modification becomes more pronounced at higher pressure and temperature conditions. Furthermore, it was shown that the development of ignition near a cold wall, for mixtures that exhibit negative temperature coefficient behavior, is very sensitive to rate of change of pressure. The near-wall ignition behavior was found also to be rather sensitive to the prevailing pressures and temperatures whose values control whether ignition will occur in the main-gas or within the thermal boundary layer.     

Enhanced DDT mechanism from shock-flame interactions in thin channels

We show experimentally and numerically that when a weak shock interacts with a finger flame in a narrow channel, an extremely efficient mechanism for deflagration to detonation transition occurs. This is demonstrated in a 19-mm-thick channel in hydrogen-air mixtures at pressures below 0.2 atm and weak shocks of Mach numbers 1.5 to 2. The mechanism relies primarily on the straining of the flame shape into an elongated alligator flame maintained by the anchoring mechanism of Gamezo in a bifurcated lambda shock due to boundary layers. The mechanism can increase the flame surface area by more than two orders of magnitude without any turbulence on the flame time scale. The resulting alligator-shaped flame is shown to saturate near the Chapman–Jouguet condition and further slowly accelerate until its burning velocity reaches the sound speed in the shocked unburned gas. At this state, the lead shock and further adiabatic compression of the gas in the induction zone gives rise to auto-ignition and very rapid transition to detonation through merging of numerous spontaneous flames from ignition spots. The entire acceleration can occur on a time scale comparable to the laminar flame time.     

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.     

Numerical simulations of the flow field ahead of an accelerating flame in an obstructed channel

The development of the unburned gas flow field ahead of a flame front in an obstructed channel was investigated using large eddy simulation (LES). The standard Smagorinsky–Lilly and dynamic Smagorinsky–Lilly subgrid models were used in these simulations. The geometry is essentially two-dimensional. The fence-type obstacles were placed on the top and bottom surfaces of a square cross-section channel, equally spaced along the channel length at the channel height. The laminar rollup of a vortex downstream of each obstacle, transition to turbulence, and growth of a recirculation zone between consecutive obstacles were observed in the simulations. By restricting the simulations to the early stages of the flame acceleration and by varying the domain width and domain length, the three-dimensionality of the vortex rollup process was investigated. It was found that initially the rollup process was two-dimensional and unaffected by the domain length and width. As the recirculation zone grew to fill the streamwise gap between obstacles, the length and width of the computational domain started to affect the simulation results. Three-dimensional flow structures formed within the shear layer, which was generated near the obstacle tips, and the core flow was affected by large-scale turbulence. The simulation predictions were compared to experimental schlieren images of the convection of helium tracer. The development of recirculation zones resulted in the formation of contraction and expansion regions near the obstacles, which significantly affected the centerline gas velocity. Oscillations in the centerline unburned gas velocity were found to be the dominate cause for the experimentally observed early flame-tip velocity oscillations. At later simulation times, regular oscillations in the unburned streamwise gas velocity were not observed, which is contrary to the experimental evidence. This suggests that fluctuations in the burning rate might be the source of the late flame-tip velocity oscillations. The effect of the obstacle blockage ratio (BR) on the development of the unburned gas flow field was also investigated by varying the obstacle height. Simulation predictions show favorable agreement with the experimental results and indicate that turbulence production increases with increasing obstacle BR.     

Use of laser-induced spark for studying ignition stability and unburned hydrogen escaping from laminar diluted hydrogen diffusion jet flames

Ignition and unburned hydrogen escaping from hydrogen jet diffusion flames diluted with nitrogen up to 70% were experimentally studied. The successful ignition locations were about 2/3 of the flame length above the jet exit for undiluted flames and moved much closer to the exit for diluted flames. For higher levels of dilution or higher flow rates, there existed a region within which a diluted hydrogen diffusion flame can be ignited and burns with a stable liftoff height. This is contrary to previous findings that pure and diluted hydrogen jet diffusion cannot achieve a stable lifted flame configuration. With liftoff, the flame is noisy and short with significant amount of unburned hydrogen escaping into the product gases. If ignition is initiated below this region, the flame propagates upstream quickly and attaches to the burner rim. Results from measurements of unburned hydrogen in the combustion products showed that the amount of unburned hydrogen increased as the nitrogen dilution level was increased. Thus, hydrogen diffusion flame diluted with nitrogen cannot burn completely.     

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.     

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.     

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.     

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 $\chi$.