Propagation limits and velocity of reaction-diffusion fronts in a system of discrete random sources

Effect of disorderness in two-dimensional discrete adiabatic combustion waves in a heterogeneous solid medium under stable regime

The effect of disorderness for the propagation of stable combustion waves in a two-dimensional discrete adiabatic system are studied by considering two systems, namely, (i) periodic and (ii) disorder. The discrete periodic system is modeled by regular arrangement of burnt and unburnt point heat sources. In contrast, the discrete disordered system is modeled by the concatenation of regular burnt and randomly distributed unburnt heat sources. Four different kinds of discrete disordered systems (S1, S2, S3, and S4) are modeled by varying the joint frequency count of unburnt heat sources without changing the domain size of the system. Results show that the disordered structure of the discrete system plays a crucial role in the combustion dynamics, shape of the combustion wave, and it affects the propagation of stable combustion waves with the manifestation of sparse and chaotic finger patterns. Quantitative analysis performed for the width and roughness of combustion front show that the disordered structure and ignition temperature (ε) of the discrete system plays a crucial role. The burn rates of discrete system are sensitive to change in structure of the system and ε. It is observed that the burn rates obtained for the discrete disordered system is always less than that of burn rates of the discrete periodic system. The burn rates calculated for the present model are compared with the available experimental data on combustion of thermite systems.

Numerical investigation of flame behavior and quenching distance in randomly distributed poly-dispersed iron dust cloud combustion within a narrow channel

In this research, the combustion of iron dust cloud through a narrow channel is simulated. Particles are randomly distributed within a rectangular control volume. Both conductive heat transferred from ignited to unignited particles and radiative heat scattered from burning particles are considered in the simulation. Radiative heat loss to the ambient gas as well as conductive heat loss to the channel walls are also taken into account. Besides, in conjunction with uniform size dust clouds, conditions in which the dust cloud is composed of poly-sized iron particles are considered to calculate flame propagation speeds and quenching distances. The results are compared with the existing experimental data. The comparison shows that they are in good agreement with the experimental measurements. Generally, an increment in dust cloud concentration leads to flame front velocity enhancement. Furthermore, flame propagation through iron powders composed of smaller particles is faster, and the quenching distance is lower. In addition, the effects of both channel wall temperatures and channel width on combustion characteristics of iron particles are investigated. The results show that flame propagation velocity usually increases with increasing the channel width. Besides, when wall temperature increases, the flame front speed increases and the quenching distance decreases.

Front roughening of flames in discrete media

The morphology of flame fronts propagating in reactive systems composed of randomly positioned, pointlike sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition of the Green's function for the diffusion equation, eliminating the need to use finite-difference approximations. The heat released from triggered sources diffuses outward from each source, activating new sources and enabling a mechanism of flame propagation. Systems of 40000 sources in a 200×200 two-dimensional domain were tracked using computer simulations, and statistical ensembles of 120 realizations of each system were averaged to determine the statistical properties of the flame fronts. The reactive system of sources is parameterized by two nondimensional values: the heat release time (normalized by interparticle diffusion time) and the ignition temperature (normalized by adiabatic flame temperature). These two parameters were systematically varied for different simulations to investigate their influence on front propagation. For sufficiently fast heat release and low ignition temperature, the front roughness [defined as the root mean square deviation of the ignition temperature contour from the average flame position] grew following a power-law dependence that was in excellent agreement with the Kardar-Parisi-Zhang (KPZ) universality class (β=1/3). As the reaction time was increased, lower values of the roughening exponent were observed, and at a sufficiently great value of reaction time, reversion to a steady, constant-width thermal flame was observed that matched the solution from classical combustion theory. Deviation away from KPZ scaling was also observed as the ignition temperature was increased. The features of this system that permit it to exhibit both KPZ and non-KPZ scaling are discussed.

Influence of discrete sources on detonation propagation in a Burgers equation analog system

An analog to the equations of compressible flow that is based on the inviscid Burgers equation is utilized to investigate the effect of spatial discreteness of energy release on the propagation of a detonation wave. While the traditional Chapman-Jouguet (CJ) treatment of a detonation wave assumes that the energy release of the medium is homogeneous through space, the system examined here consists of sources represented by δ functions embedded in an otherwise inert medium. The sources are triggered by the passage of the leading shock wave following a delay that is either of fixed period or randomly generated. The solution for wave propagation through a large array (10^{3}-10^{4}) of sources in one dimension can be constructed without the use of a finite difference approximation by tracking the interaction of sawtooth-profiled waves for which an analytic solution is available. A detonation-like wave results from the interaction of the shock and rarefaction waves generated by the sources. The measurement of the average velocity of the leading shock front for systems of both regular, fixed-period and randomized sources is found to be in close agreement with the velocity of the equivalent CJ detonation in a uniform medium, wherein the sources have been spatially homogenized. This result may have implications for the applicability of the CJ criterion to detonations in highly heterogeneous media (e.g., polycrystalline, solid explosives) and unstable detonations with a transient and multidimensional structure (e.g., gaseous detonation waves).