A.C. McIntosh

PRESSURE DISTURBANCES OF DIFFERENT LENGTH SCALES INTERACTING WITH CONVENTIONAL FLAMES

The theory of large activation energy asymptotics is used to model the interaction of pressure disturbances characterised by different length scales with conventional flames. Byconventional flames it is understood that the deflagration Mach number is low and of the order of where 0 is the non dimensional activation energy and s is a positive power arising from the detail of a (global) kinetic scheme. By denoting the paper explores the coupling that exists between pressure disturbances and flames for medium to short wavelengths. that is with N in the range M −l to 1. The work complements that which has mainly been achieved assuming N ≫ M −1 (long wavelengths). As N becomes smaller the coupling from pre-heat and chemical zones becomes more pronounced. This work first deduces jump conditions across the flame zone for N ≈ M −1 with density variations included (up to now these have been ignored). The foundation is then laid for N ≈ 1/(02 M) (i.e. shorter wavelength) coupling and it is shown that a different un...

Feedback processes in cellulose thermal decomposition. Implications for fire-retarding strategies and treatments.

A simple dynamical system that models the competitive thermokinetics and chemistry of cellulose decomposition is examined, with reference to evidence from experimental studies indicating that char formation is a low activation energy exothermal process and volatilization is a high activation energy endothermal process. The thermohydrolysis chemistry at the core of the primary competition is described. Essentially, the competition is between two nucleophiles, a molecule of water and an −OH group on C6 of an end glucosyl cation, to form either a reducing chain fragment with the propensity to undergo the bond-forming reactions that ultimately form char, or a levoglucosan end-fragment that depolymerizes to volatile products. The results of this analysis suggest that promotion of char formation under thermal stress can actually increase the production of flammable volatiles. Thus, we would like to convey an important safety message in this paper: in some situations where heat and mass transfer is restricted in cellulosic materials, such as furnishings, insulation, and stockpiles, the use of char-promoting treatments for fire retardation may have the effect of increasing the risk of flaming combustion.

Linear stability analysis of laminar premixed spray flames

We present an analysis of instability to transverse perturbations of laminar premixed plane spray flames. To this end, a thermal‐diffusional model of a flame front propagating through an overall fuel‐rich or fuel‐lean droplet‐vapour‐air mixture is presented. The fuel droplets are permitted to vaporize at a finite rate so that their interaction with, and possible traversal of, the flame front is accounted for. After establishing steady‐state solutions by means of high activation energy asymptotics, a detailed linear stability analysis is carried out in order to determine neutral stability boundaries. For the fuel‐rich case, it is demonstrated that under certain circumstances a spray flame may be cellular even though its equivalent non‐spray flame is completely stable. In addition, even when the non‐spray flame is itself cellular, the equivalent spray flame will have a finer cellular structure. To our knowledge, these results are the first theoretical qualitative verification of sparse but compelling experimental evidence from the literature. The main effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading, the latent heat of vaporization and the vaporization coefficient on the critical wavenumber associated with cellularity provides strong evidence of the major role of the heat‐loss mechanism in these sprayrelated phenomena. For fuel‐lean spray flames, it is found that the heat‐loss mechanism manifests itself prominently via the pulsating stability boundary which penetrates into the region of realistic Lewis numbers, thus verifying recent experimental observations of pulsating cellular spray flames. Finally, the cellularity of the spray flames, with their attendant increase in flame front area, suggests a plausible rationale for those circumstances in which burning velocity enhancement, induced by the use of a spray of droplets, was observed experimentally.

The linearised response of the mass burning rate of a premixed flame to rapid pressure changes

ABSTRACT An investigation is made into the response of the mass burning rate of a premixed flame to small but sharp changes in pressure. In this paper a fast time scale is considered such that (K1 = thermal diffusivity, u01 1 = initial burning velocity, l1 a = a typical acoustic length, a01 1 = frozen sound speed, θ = nondimensional activation energy). Previous studies by the author (Mclntosh 1990)and by other researchers (e.g. Ledder and Kapila 1991) have considered the case of r = 1 which is the usual value corresponding to audible resonance of flames in tubes, burner ports etc. However the case r = Θ2 (Mclntosh 1991)is a most interesting and distinct case since then the fast time scale alters the inner reaction zone which consequently obeys a different and essentially unsteady diffusion-reaction equation. The mass burning rate is then on an appreciably larger scale. The time response of the mass burning rate to pressure fluctuations at this fast time scale is governed in general by a non-linear partial...

A numerical study of the vorticity field generated by the baroclinic effect due to the propagation of a planar pressure wave through a cylindrical premixed laminar flame

The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b ) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.

Thermal explosion in a combustible gas containing fuel droplets

An original physical model of self-ignition in a combustible gas mixture containing liquid fuel droplets is developed. The droplets are small enough for the gas-droplet mixture to be considered as a fine mist such that individual droplet burning is subsumed into a well-stirred, spatially invariant burning approximation. A classical Semenov-type analysis is used to describe the exothermic reaction, and the endothermic terms involve the use of quasi-steady mass transfer/heat balance and the Clausius-Clapeyron evaporative law. The resulting analysis predicts the ignition delay which is a function of the system parameters. Results are given for typical dynamical regimes. The case of different initial temperatures for droplets and gas is highly relevant to gas turbine lean blow-out and re-ignition.

Autoignition of combustible fluids in porous insulation materials

Abstract The leakage of combustible fluids into the lagging of pipework in the process engineering industry can be very hazardous because of the increased residence time for oxidation as the liquid resides in the porous medium and also the substantially modified heat and mass transfer rates when compared with ignition at hot surfaces. The exothermic reaction can lead to ignition or at least severe self-heating with the consequent damage of pipework, etc. Experiments have been performed to simulate this hazard. The thermal behavior of a number of combustible liquids placed in porous material has been monitored and evidence is presented in this work that self-heating can indeed take place. It has been found that autoignition occurs at an important “watershed” oven temperature that is related to the volatility of the combustible fluid. A mathematical model for the autoignition of combustible liquid in an inert porous material is presented. The simple model takes a spatially uniform approach to both the energy equation and the liquid equation for the fluid and predicts a watershed temperature such that for a given concentration of fluid in the porous material, the thermal behavior of the system alters abruptly. For all practical purposes, thermal runaway is predicted beyond this watershed condition even though the classical Semenov theory simply predicts an eventual decay to a stable steady state, with no strict “criticality” prediction. The watershed temperature is shown to depend on volatility and reactivity.

Baroclinic distortion of laminar flames

One of the most important divisions in studies of premixed gaseous combustion is that between the theoretically much favoured laminar flames, and the more commonly observed case of turbulent burning. Laminar premixed flames clearly represent much simpler cases for theoretical and numerical study. Conversely experimental investigations are much simpler in the case of turbulent combustion due to the inherent instability of laminar fluid flows. One mechanism which can effect the transition from laminar to turbulent combustion is baroclinicity (i. e. the non-alignment of pressure and density gradients). A laminar deflagration, or slow flame, may be thought of as a reaction front which propagates at a low Mach number and whose associated pressure field is therefore close to uniformity. On the other hand, very steep density gradients are associated with the rapid temperature increase due to the exothermic chemical reaction. (Note that a typical deflagration thickness is of the order of 1 mm, and densities may decrease by factors of between five and ten in going from unburnt to burnt gas.) Externally induced pressure disturbances, which are almost universally present in practical combustion systems, can introduce a baroclinic effect whenever a steep pressure gradient interacts with a flame front in such a way that the former is misaligned with the density gradient associated with the latter. The differential acceleration of fluid elements can produce significant rotational motion and, if this field of vorticity is sufficiently strong, a laminar flame front may be broken up and the transition to turbulent burning may result. This scenario was clearly demonstrated in an experiment done by Markstein (1963) that involved the double passage of a large amplitude planar pressure signal across an expanding spherical flame bubble in a shock tube. The laminar flame front was completely obliterated, and the evolution to fine grain turbulent combustion was revealed. In the current paper we report on numerical simulations of a number of similar experiments. Although we are here restricted to two space dimensions and cannot therefore investigate fully turbulent behaviour, these simulations do reveal qualitatively similar behaviour to that found in the early stages of the Markstein experiment. It has been possible to repeat the simulations for a variety of different flames, so that the effects of the various processes (in particular the chemical reaction and the ther-moviscous diffusion) can be assessed. Attention is also given to the question of the grid dependency of the numerical solutions obtained.

Thermokinetic Models for Simultaneous Reactions: a Comparative Study

Two dynamical thermokinetic systems for simultaneous reaction models of polymer decomposition are compared. In the independent-parallel model, the common reactant is divided explicitly between the reactions, and in the competitive model the entire reactant mass is available to both reactions. Elementary bifurcation analyses show that the two models give quite different predictions of the thermal behaviour of simultaneous reaction systems. The properties of derivative thermogravimetric curves for competitive and independent thermokinetic models are discussed, with reference to experimental data for the thermal decomposition of cellulose.

The bombardier beetle and its use of a pressure relief valve system to deliver a periodic pulsed spray

In this paper the combustion chamber of the bombardier beetle is considered and recent findings are presented which demonstrate that certain parts of the anatomy are in fact inlet and outlet valves. In particular, the authors show that the intake and exhaust valve mechanism involves a repeated (pulsating) steam explosion, the principle of which was up till now unclear. New research here has now shown the characteristics of the ejections and the role of important valves. In this paper numerical simulations of the two-phase flow ejection are presented which demonstrate that the principle of cyclic water injection followed by water and steam decompression explosions is the fundamental mechanism used to create the repeated ejections.