J. Griffiths

Ignition phenomenology and criteria associated with hotspots embedded in a reactive material

Abstract A numerical study is presented of the phenomenology of ignition, and initiation of combustion waves, in a model representing a spherical power source embedded in a concentric spherical volume of combustible material of relatively low exothermicity. For simplicity, one-step chemistry is assumed, and diffusion of oxygen or gaseous products is neglected. The results show unexpected behaviour for small-sized power sources, in which, over a range of source radii, there are two distinct critical values for the power, with an apparently “safe” region occupying some of the range between them. Possible safety implications for chemical plant operation are discussed.

The Ignition of Low-Exothermicity Solids by Local Heating

In this paper we bring together a number of recent studies associated with the burning of low-exothermicity porous materials that are inadvertently, or otherwise, exposed to a maintained heat source (hotspot). Additionally, we provide some new results in the form of dimensionless ignition criteria, which allow us to generalize previous results to a broader class of materials and to larger sample sizes. It is shown that systems of the type described can be represented by a hierarchy of mathematical models, depending on whether oxygen is in limited supply, is not required (as in the case of thermal decomposition), and/or a significant volume of gaseous products is present. We summarize the behaviour of systems in which gas motion through the solid pores has a negligible effect, including cases where the burning is dependent on a limited supply of oxygen. The effects of geometry and initial-boundary conditions are discussed. Finally, for reactions involving gaseous products, we present numerical solutions to a system of equations that incorporates the gas motion through the solid pores by employing Darcys law. In comparison with the previous cases, it is demonstrated that ignition of low-exothermicity materials is more difficult to achieve (a larger hotspot heat-flux is required), essentially because of transportation of heat by advection towards the unburnt solid, and, consequently, increased reactant depletion. Furthermore, ignition will always take place away from the hot-spot surface; this is in complete contrast to highly exothermic materials, in which reactant depletion is negligible during the early stages of ignition, and in which ignition occurs at the hotspot boundary.

Measurements of reactant temperature and free-radical concentrations during the oscillatory combustion of hydrogen and carbon monoxide in a CSTR

Abstract Experimental studies in which the phase relationship between a reactive intermediate concentration and reactant temperature during the gas-phase, oscillatory combustion of hydrogen + carbon monoxide mixtures in a non-adiabatic CSTR are reported. This combustion reaction and its counterpart, hydrogen oxidation, constitutes the simplest of the non-isothermal, quadratic autocatalytic systems. The hydroxyl radical (OH) is a primary propagating species. Measurements of the laser-induced absorption spectrum of OH during oscillatory reaction led simultaneously, via data capture and analysis by computer, to absolute concentrations of the species and to the reactant temperature. The results show that there is a considerably reduced reactivity of the carbon monoxide-containing reaction when compared with the results obtained previously from hydrogen oxidation. The OH concentration and reactant temperature remain in phase during the oscillatory combustion.

An approximate model for the ignition of reactive materials by a hot spot with reactant depletion

In this paper, we present a mathematical model to describe the ignition of a reactive material subject to a known heat input at a given radius. By current methods, the full solution is not readily solvable analytically. The main purpose of this work is to pose the right questions for this complex phenomenon, which is yet some way from total solution. An approximate solution to the model equations is presented, and a possible physical explanation for the finding that ignition behaviour is suppressed for small radius hot spots.

Initiation of combustion waves in solids, and the effects of geometry

In a recent paper Weber et al. [9] examined the propagation of combustion waves in a semi-infinite gaseous or solid medium. Whereas their main concern was the behaviour of waves once they had been initiated, we concentrate here on the initiation of such waves in a solid medium and have not examined in detail the steadiness or otherwise of the waves subsequent to their formation. The investigation includes calculations for finite systems. The results for a slab, cylinder and sphere are compared. Critical conditions for initiation of ignition by a power source are established. For a slab the energy input is spread uniformly over one boundary surface. In the case of cylindrical or spherical symmetry it originates from a cylindrical core or from a small, central sphere, respectively. The size of source and reactant body is important in the last two cases. With the exception of the initial temperature distribution, the equations investigated are similar in form to those of Weber et al. [5,9] and, as a prelude to the present study, with very simple adaptation, it has been possible to reproduce the results of the earlier work. We then go on to report the result of calculations for the initiation of ignition under different geometries with various initial and boundary conditions.

The effect of oxygen starvation on ignition phenomena in a reactive solid containing a hot-spot

In this paper, we explore the effect of oxygen supply on the conditions necessary to sustain a self-propagating front from a spherical source of heat embedded in a much larger volume of solid. The ignition characteristics for a spherical hot-spot are investigated, where the reaction is limited by oxygen, that is, reactant + oxygen → product. It is found that over a wide range of realistic oxygen supply levels, constant heating of the solid by the hot-spot results in a self-propagating combustion front above a certain critical hot-spot power; this is clearly an important issue for industries in which hazard prevention is important. The ignition event leading to the formation of this combustion wave involves an extremely sensitive balance between the heat generated by the chemical reaction and the depletion of the reactant. As a result, for small hot-spot radii and infinite oxygen supply, not only is there a critical power above which a self-sustained combustion front is initiated there also exists a power beyond which no front is formed, before a second higher critical power is found. The plot of critical power against hot-spot radius thus takes on a Z-shape appearance. The corresponding shape for the oxygen-limited reaction is qualitatively the same when the ratio of solid thermal diffusion to oxygen mass diffusion (N) is small and we establish critical conditions for the initiation of a self-sustained combustion front in that case. As N gets larger, while still below unity, we show that the Z-shape flattens out. At still larger values of N, the supercritical behaviour becomes increasingly difficult to define and is supplanted by burning that depends more uniformly on power. In other words, the transition from slow burning to complete combustion seen at small values of N for some critical power disappears. Even higher values of N lead to less solid burning at fixed values of power.

Ignition and combustion of low-exothermicity porous materials by a local hotspot

We present numerical investigations of a spherically symmetric model for the ignition and subsequent combustion of low-exothermicity porous materials exposed to a constant, continuous heat source. We account simultaneously for oxidant, the gas-dynamic processes, including a gaseous product of reaction, and a solid product that is allowed to assume different physical properties from the solid reactant. For external conditions that are typical of natural convection, the model exhibits striking novel behaviour, including the possibility of a potentially dangerous high-temperature ‘burnout’ at the external surface of the material, which triggers a reverse combustion wave propagating from the outer surface of the solid towards the heat source. This phenomenology is controlled largely by the diffusion of oxygen entering the system. We identify the effects that convection and product properties have on combustion of the solid, particularly on the formation of a reverse wave. Applications of the approach to specific problems are discussed and future work is outlined.

Spatial effects in the thermal runaway of combustible fluids in insulation materials

The thermal runaway and eventual ignition of flammable fluids in lagging materials has occurred with sufficient frequency for there to be considerable awareness of this problem in the process engineering industry. Earlier (mainly spatially invariant) models are here modified to include the important effect of diffusion. The aim is to identify boundaries in parameter space where ignition will or will not occur. In this paper, a model of the three main contributing quantities (temperature, fuel and oxygen concentration) is considered which includes exothermic oxidation and endothermic evaporation/desorption processes and primarily centres on the energy balance equation. The shape of the ignition boundary is found to depend crucially on a key value of the ratio of thermal diffusion to mass diffusion of oxidant (inverse Lewis number). The critical value of this ratio is in fact size-dependent and beyond a certain value, ignition will be suppressed.

Experimental studies of the oscillatory combustion of hydrogen in a stirred flow reactor

Experimental studies of the phase relations between H atoms, OH radicals and reactant temperature during the gas-phase, oscillatory combustion of hydrogen in a well-stirred flow reactor are reported. Absolute concentrations of the OH radical and the reactant temperature were measured in absorption from the vibrational-rotational structure of the laser-induced, electronically excited, OH spectrum . Relative concentrations of H atoms were obtained by multiphoton ionization, also induced by a laser. The hydrogen atoms reached their maximum concentration first during the oscillatory combustion, rising to a sharp peak followed by a rapid decay within several milliseconds. The OH radicals reached their maximum concentration about 1 ms after the H atoms. The maximum of the reactant temperature was in phase with the hydroxyl radicals. Experimental and numerical studies of the interaction that occurs between oscillations in a pair of coupled reactors are also presented.

Criteria for Autoignition of Combustible Fluids in Insulation Materials

Criteria have been investigated for the conditions at which a ‘lagging fire’ may occur when a flammable liquid penetrates and is dispersed within insulation material surrounding a hot pipe. The conditions at which a Frank-Kamenetskii thermal ignition criterion should be replaced by one derived from the heat release rate versus fluid evaporation rate were deduced. These conditions were related to the decreasing enthalpy of vaporization of the fluid. Practical investigations were based on formal ‘cube test’ methods for thermal ignition. The theory was tested against the behaviour of n -C 16 H 34 , n -C 18 H 38 and n -C 20 H 42 , which represent alkanes of mid-range volatility, and also with reference to squalane (C 30 H 62 ), which is representative of highly involatile alkanes.