Diffusion controlled smoulder propagation in a thin slab

Complex variable techniques are used to determine the shape of the smouldering reaction front and the concentration of the oxidizer behind the front for steady smoulder propagation in a solid slab of exothermically reacting material. It extends an earlier free boundary problem of Adler and Herbert which considered diffusion controlled smoulder propagation in a half-space. The region behind the reaction front is assumed to be porous, the oxidizer diffusing from both planar surfaces to the front, where its concentration vanishes. Suitable scaling allows the oxidizer concentration to be expanded in powers of a small parameter. The resulting coupled differential equations for the coefficients are solved in terms of functional equations. Some consideration is given to the regions where the front meets the planar surfaces. It is shown that, close to the leading edge, the surface concentration varies monotonically with distance from the edge.     

Similarity solutions of a strong shock wave propagation in a mixture of a gas and dusty particles

The similarity solutions of a strong shock wave propagation in a mixture of a gas and small solid particles have been investigated. Similarity solution exists only when the shock is very strong and the surrounding medium is of a constant density and at rest and with negligible counterpressure. The non-dimensional fundamental equations are derived and studied. The results depend on three non-dimensional parameters; i.e. (i) the ratio of the specific heats of the gas γ, (ii) the mass concentration of the solid particles k_p in the mixture and (iii) the ratio of the density of the solid to that of initial density of the gas G. Numerical solutions for various values of γ k_p and G are presented and discussed. The speeds of the shock wave front and its location with various energy releases are given.     

The Effect of the Variability of Density on the Propagation of Heat in a Gas

The qualitative and quantitative effect of compressibility on the propagation of heat in an ideal gas in the absence of mass forces is investigated. Based on the assumption of the constancy of pressure throughout a closed cavity, a physical and a mathematical models are constructed for a flat layer of gas. Criteria of similarity are revealed which characterize the propagation of heat in the gas being compressed. Using the flat layer as an example, the processes of the propagation of heat in gas and solid are compared.     

Numerical Simulation of Detonation and Multi-Material Interface Tracking

In this paper, we report high resolution simulations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third-order TVD Runge-Kutta time stepping method to examine the features of the detonation for gas and condensed explosives. A two-stage chemical reaction model and an ignition and growth model are employed to describe the chemical reaction process for gas and condensed explosives. Based on the Steger-Warming vector flux splitting method, a splitting method is employed when the vector flux does not satisfy the homogeneity property for simulating detonation wave propagation for condensed explosives. The sensibility of flame propagation process and explosion overpressure on obstacles is also numerically performed. Meanwhile, an interface tracking algorithm is developed and coupled with a two-dimensional multi-material code indigenously for simulating the response of materials to impact, shocks and detonations. Numerical experiments are performed to investigate the influences of liner cone angle, wall thickness and initiation mode on shaped charge jet formation process. The results of calculations show good agreement with experimental results, and indicate that the interface treatment algorithm is especially suitable for simulating explosive loading on thin-wall structure such as shape charges.     

Diffusion-controlled smoulder propagation in a composite slab

The steady propagation of a thin smouldering front parallel to the faces of a composite reactive slab has been considered. The slab consists of a double layer of solid with differing densities. As the smouldering front progresses into the solid it leaves behind an inert porous medium through which oxidizer is able to diffuse to the front. It is assumed that the reactive solid is sufficiently dense for no oxidizer to be present. The oxidizer concentration on one face of the slab is specified, the other being impervious to the transport of reactants. Dimensionless equations and boundary conditions are obtained for the concentration of oxidizer in the porous medium. These are solved to first order by use of a complex-variable method and a hodograph transformation giving the shape of the smouldering front for various parameter combinations. The analysis is extended to the case where the layers are of unequal thickness. Simple expressions for the shape of the front and the oxidizer concentration are obtained when one layer thickness is large. The model here considered is a first step in a more comprehensive analysis of smouldering in a non-uniform medium.     

An in situ Study of the Kinetics of a Solid-Phase Reaction Activated by the Energy of Elastic Stresses Arisen upon the Formation of the Cu/As<Subscript>2</Subscript>Se<Subscript>3</Subscript> Nanosized Film Structure

For the first time, the kinetics of a solid-phase chemical reaction activated by the energy of elastic stresses generated upon the formation of the Cu/As₂Se₃ nanosized film structure is investigated in situ. It is shown that the time at which a solid-phase chemical reaction starts, as well as the voltage of the Cu/As₂Se₃ heterolayer, significantly depends on the thickness of the As₂Se₃ film. At a critical thickness of the As₂Se₃ film, which is equal to 110 nm, a threshold value of the energy of elastic stresses is achieved. Relaxation of this energy over new defects (micropores and microcracks) generated in the film system leads to the activation of a solid-phase chemical reaction and an increase in its rate. A mechanism of the operation of a positive feedback between the chemical reaction in a solid phase and elastic stresses is proposed.     

CVI热解炭微观结构的参数控制研究

化学气相渗透(CVI)制备炭/炭复合材料涉及气体扩散和气相沉积2个过程,其工艺控制决定炭纤维坯体的增密速度、热解炭的结构和炭/炭材料的性能.工艺过程的控制主要有4类参数:第一参数包括沉积温度、系统压力、碳源浓度、碳源分压等,第二参数包括均相反应、异相反应和滞留时间等,第三参数为A_s/V_R,也就是沉积基体的表面面积与炉内气体的自由体积之比,以及目前以计算机模拟为主要手段的"第四参数"的研究.在固体表面沉积热解炭的科学研究已经持续了几十年,但至今为止还没有形成一种完善的表面沉积机理,分析了CVI工艺参数发展的趋势,说明了对热解炭微观结构形成机理的认识是一个不断深入的过程.     

A multi-scale approach to the propagation of non-adiabatic premixed flames

Flame propagation involves physico-chemical processes that occur over a range of temporal and spatial scales. By use of a multi-scale analysis it is shown that diffusion processes occurring on relatively small scales can be resolved analytically when the overall activation energy of the chemical reactions is large, thus providing, by asymptotic matching, explicit conditions for the state of the gas and for the flow field across the flame zone. The mathematical formulation on the larger hydrodynamic scale reduces to a free-boundary problem, with the free surface being the flame front. The front propagates into the fresh unburned gas at a rate that depends on both the local strain that it experiences and the local curvature, with coefficients that depend on the diffusion rates of heat and mass, the equivalence ratio of the mixture and the chemical kinetic parameters. The simplified model, properly termed a hydrodynamic model, involves the solution of the Navier Stokes equations with different densities and viscosities for the burned and unburned gas. The present work extends earlier studies by including volumetric heat loss, such as radiative loss, which affects the dynamics and may lead to flame extinction.     

Properties of Wave Propagation in a Gel-type Belousov–Zhabothinsky Reaction under Micro-gravity

The Belousov–Zhabothinsky (BZ) reaction is a chemical reaction which exhibits spatial as well as temporal pattern formation. Being an excitable medium, it can be influenced by even small external forces. One of these small forces which under ground conditions permanently is given is gravity. The gravity dependence of the BZ-reaction has been investigated in some detail up to now, and it has been found that especially the propagation velocity of waves in thin layers of fluid BZ-medium depends significantly on gravity-amplitude and -orientation. This finding has been mainly assigned to an interaction of gravity with diffusion and convection in the medium at the wave front, and consequently it has been stated that the propagation of waves in gels of BZ-medium is not significantly gravity dependent. We have now done more detailed experiments and have been able to show that also in gels the propagation velocity of BZ-waves is altered by gravity, but less than in fluid systems. Experiments have been performed in a lab centrifuge, a sounding rocket experiment and a parabolic flight mission.     

Computational simulation of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper primarily deals with the computational aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. After the dimensionless governing partial differential equations of the non‐isothermal chemical dissolution‐front instability problem are briefly described, the formulation of a computational procedure, which contains a combination of using the finite difference and finite element method, is derived for simulating the morphological evolution of chemical dissolution fronts in the non‐isothermal chemical dissolution system within two‐dimensional fluid‐saturated porous media. To ensure the correctness and accuracy of the numerical solutions, the proposed computational procedure is verified through comparing the numerical solutions with the analytical solutions for a benchmark problem. As an application example, the verified computational procedure is then used to simulate the morphological evolution of chemical dissolution fronts in the supercritical non‐isothermal chemical dissolution system. The related numerical results have demonstrated the following: (1) the proposed computational procedure can produce accurate numerical solutions for the planar chemical dissolution‐front propagation problem in the non‐isothermal chemical dissolution system consisting of a fluid‐saturated porous medium; (2) the Zhao number has a significant effect not only on the dimensionless propagation speed of the chemical dissolution front but also on the distribution patterns of the dimensionless temperature, dimensionless pore‐fluid pressure, and dimensionless chemical‐species concentration in a non‐isothermal chemical dissolution system; (3) once the finger penetrates the whole computational domain, the dimensionless pore‐fluid pressure decreases drastically in the non‐isothermal chemical dissolution system.     

Modeling study of migration-driven lateral instability in autocatalytic systems

The lateral stability of reaction fronts in simple autocatalytic models with the components carrying various charges is investigated when the system is exposed to an inhomogeneous electric field parallel to the direction of propagation. The enhanced migrational flux of the reactant destabilizes the planar front giving rise to a cellular structure because the electric field strength is greater on the reactant side of the reaction front. The onset of instability depends not only on the charge difference between the reactant and the autocatalyst but also on the variation of specific conductance in the course of the reaction, which results in a difference in electric field strength on the opposite sides of the reaction front.     

Reaction Driven Elastic Waves in Solid Media

Chemical reactions and phase transformations couple in solid systems with the stress fields. When reaction rates become of the same order as the rate of relaxation of mechanical perturbations, the reactions can stabilize elastic waves in the system. Density varies with temperature and conversion and since the elastic waves are driven by the gradients in temperature and conversion, these source terms travel with the same speed as the reaction front. A model is presented for elastic waves in solid media, driven by a moving source term that is well approximated by a delta function. The propagation velocity of this source is constant, but it can propagate either subsonically or supersonically. The effects of precompressing the sample, applying a force at one boundary, and varying the strength of the source term with time are included in the discussion. The model is useful to study transformation reactions under shock-compression, ultrafast deflagrations, and detonations in the solid phase.     

Centrifugal effects on combustion synthesis of (Ti-B-C) compound system

A centrifugal force plays an important role on the control of combustion synthesis. In the present work, the data of reaction propagation rates obtained by changing the direction of reaction propagation and centrifugal force are evaluated in order to make clear the effect of centrifugal force on reaction propagations and product formation. As a result, the reaction propagation rate in the case of the direction of centrifugal force inverse to reaction propagation is larger than that in the case of the same direction, and product grains become smaller in size. It is confirmed that the centrifugal effect is much larger for the present combustion synthesis process in the case that the reaction propagates inversely to the direction of centrifugal force. Since molten titanium near combustion front tends to coalesce into larger drops in that case, reactants of boron and carbon would diffuse more sufficiently into titanium.     

An investigation of the ignition manner effects on combustion synthesis

The multi-point ignition of combustion synthesizing NiAl compound created by computational means has been analyzed in this article. Since the combustion reaction of Ni and Al is a low exothermic reaction, it has been found that the combustion front hardly propagates in order to complete the reaction. In this study, the reaction is subsequently ignited at different points or it is simultaneously ignited at several points to help the combustion front to propagate completely. The different positions of ignition are found to influence the temperature profiles and an increase in the number of ignition points is noted to increase the propagation velocity. In addition, the effect of a second ignition of the extinguished combustion reaction is also studied. It is noted that the position and time of the second ignition has dramatically influenced on the propagation velocity and combustion temperature, thus resulting in different grades of reactions. The extent of reacting for each double-ignition condition is calculated in order to generate the reacting maps. From the reacting maps generated in this study, the appropriate double-ignition condition can be chosen to synthesize homogeneous products.     

Spinning front formation in fuel gas-air flame

The method of forming a spinning front of the flame in a propane-air mixture in a flat gap between two plates is proposed. It is shown that the spinning flame fronts (SFFs) are formed in gas mixtures with an excess fuel component and are due to the decay of an initial cylindrical front. It is established that the decay of a cylindrical front is related to the onset of a thermodiffusion instability, which is accompanied by the suppression of the majority of small perturbations on the flame surface and results in the development of only two of these perturbations. The subsequent evolution of the fields of temperatures, concentrations, and velocities in the vicinity of the leader points of developing perturbations results in the formation of an SFF, which resembles extended arc-shaped whiskers. Temporal variations in the angular and tangential velocities of SFF propagation are determined.     

The enhancement of weakly exothermic polymerization fronts

The propagation of one-dimensional waves resulting from chemical reactions in a sandwich-type two-layer setting is considered. One layer, termed the polymerization layer, contains the monomer and initiator molecules needed for the initiation of a self-propagating polymer front. The other layer will be referred to as the enhancement layer, and it contains the necessary reactants to support a highly exothermic self-propagating reaction wave. Heat exchange occurs between the layers, and as a result, there is a net diffusion of heat away from the region undergoing the more exothermic reaction. As frontal polymerization (FP) reactions are known not to be very exothermic, an overall transfer of heat from the enhancement layer into the polymerization layer takes place. An analysis of the basic state of the system is carried out to investigate the effect of heat transfer on the polymerization reaction. An enhancement layer is shown to promote FP. This analysis is applicable to the manufacture of thin polymer films by FP.     

Modeling of the mechanical treatment of a solid reactant under active gas in the high-energy mill on the example of the titanium-gaseous nitrogen system

A mathematical model for calculating the dynamics of product formation (titanium nitride) in the gas (nitrogen) medium during milling and activation of a solid reactant in the high-energy mill was built based on a new macrokinetic theory of mechanochemical synthesis. For the first time, the model uses an approach based on the theory of short-lived active sites to take into account the intensification of chemical processes in the volume of the solid and on the surface formed during destruction. The model can calculate the following macroscopic parameters: temperature, depth of chemical transformations, size of particles, gas pressure, structural defects of particles (excess energy). An analytical formula for determining the mechanochemical reaction on an active surface was derived. The modelling results were compared with the known experimental data.     

Shock front analysis for axial shear wave propagation in a hyperelastic incompressible solid

Summary A wavefront analysis is employed to study the propagation of axial shear waves in an incompressible hyperelastic solid, whose strain energy function is expressible as a truncated power series in terms of the basic invariants of the left Cauchy-Green tensor. Waves are generated by the application of an axial shear stress at the surface of a cylindrical cavity in an unbounded medium. Depending on the nature of the boundary condition, an acceleration front or a shock front propagates from the boundary of the cavity. For an acceleration front, the coefficients in the wavefront expansion satisfy a sequence of transport equations which can be solved analytically. For a shock front, a wavefront analysis gives approximate formulas for the wave speed, shock front and intensity of the various field variables at the front. As well, our shock front analysis is used to devise a method of estimating the breaking distance of a shock front. In order to test the validity of the results of our wavefront analysis, numerical solutions are obtained for waves initiated by a step function or by a finite duration pulse at the boundary. Our numerical solutions are found by using a recently proposed relaxation scheme for systems of conservation laws.     

Stress fields of solid flow in a model blast furnace

The computational fluid dynamics–discrete element method approach, supported by an averaging technique, has been employed to quantitatively investigate the stress distributions of solid flow in a model blast furnace (BF). The results indicate that large normal stresses are mainly observed in the lower central part of the BF, whilst small normal stresses in the vicinity of the raceway. In the upper part, the vertical normal stress varies little horizontally in the central region but reduces a bit near the wall, whereas the horizontal normal stress has a relatively uniform distribution on the whole cross section. The shear stress has its largest magnitude in two symmetrical regions close to the stagnant zone. The couple stress can be ignored except for the regions close to the walls. The stress and couple stress are both affected by gas flow rate. In particular, increasing gas flow rate will decrease the magnitude of the stress and couple stress. The internal friction coefficient is not dependent on the inertial number for the solid flow in a BF, but it may rely on the inertial number in some specific flow regions for the cases without gas and with low gas flow rates.     

A numerical study of the effect of heterogeneities in composition on micropyretic synthesis

Micropyretic synthesis is a technique whereby a material is synthesized by the propagation of a combustion front across a powder. Composition variations in reactants and diluent are common during micropyretic synthesis when powders are mixed and the conventional modeling treatments thus far have only considered uniform systems. Composition variations are thought to result in the local variations of such thermophysical/chemical parameters for the reactant as density, heat capacity, and thermal conductivity; the result is changes in the combustion temperature, propagation velocity, and propagation pattern of a combustion front. This study investigates the impact of composition variations during micropyretic synthesis with Ni + Al. Correlations of variations in the reactants and diluent with the propagation velocity and combustion temperature are both studied by a numerical simulation.