Search

Intentional introduction of alien plant species through increased global trade and movement of people worldwide has contributed to the current problem of invasion by alien plant species and their significant impacts to primary production, the environment, human health and society. Weed Risk Assessment (WRA) systems have been developed to help screen out those potentially invasive alien plant species prior to their introduction (i.e. pre-border) and manage those that pose a risk once they arrive (i.e. post-border Weed Risk Management (WRM)). Despite some developed countries (e.g. Australia and New Zealand) having successfully developed, tested, and implemented WRA systems, broad-scale application in developing countries that have open and porous borders is yet to occur. This is, in part, because the WRA approach developed is predicated on the assumption that effective management of the movement of goods and people across borders is both practical and achievable, and if not then a post-border WRM approach is the ‘best’ option. Here, we examine how pre-border WRA and post-border WRM systems can be implemented in developing countries with open and porous borders using insights from the land-locked country of Bhutan to highlight the issues and practicalities of implementing a risk assessment approach for alien plants. Firstly, we examine the limitations and benefits associated with implementing a WRA approach at the border in countries with open and porous borders. Secondly, we explore the limitations and benefits of managing the risks using a post-border WRM approach. This assessment revealed that whilst some aspects of a both pre- and post-border systems could be adopted in countries with open and porous borders, it was impractical to adopt the pre-existing systems in such instances. Thus, many countries may adopt a hybrid approach for which no guidance is currently available. To address this issue, we propose a formal hybrid weed risk model, using elements of both pre- and post-border systems based on the individual circumstances of the country. To account for such circumstances, we constructed a series of decision trees to help managers and policy makers determine the most appropriate hybrid model. These decision trees provide a standardised structure for identifying and justifying the elements used in a hybrid model for managing the risk from alien plants in countries with open and porous borders. The adoption of such a hybrid approach will help prevent and manage potential invasive alien plant species in these countries through a more formalised risk assessment approach.

Biological invasions are a serious threat globally, but particularly in developing countries. Bhutan is unique among South Asian countries in that it has a rich biodiversity, and its people have a ‘sacred’ responsibility to protect the environment and native biodiversity; conversely it is also considered a ‘crisis ecoregion’ because of significant threats to biodiversity from anthropocentric activities. Managing biological invasions is difficult without a comprehensive baseline of the alien species present. An alien plant inventory for Bhutan was created by examining an extensive array of information and data sources such as herbaria records, published floras, unpublished documents, and from personal communications. The alien plant flora including cultivated taxa in Bhutan comprises 139 families, 545 genera and 964 species. Of these, 626 species occur only in cultivation, whilst the other 338 species occur in the wild (spontaneous); 131 (39%) casuals, 103 (31%) naturalised and 101 (30%) invasive. The major of naturalised alien plants were introduced as pasture species (32%), ornamentals (24%) and from unintentional sources (22%). Whilst, the major of invasive species were introduced unintentionally (76%), as ornamentals (15%) and pasture species (3%). Because a large proportion of alien plants have been deliberately introduced, implementation of both pre-border weed risk assessment and post-border weed risk management approaches can be effective in Bhutan, despite the country’s open and porous borders. Such a biosecurity approach could also be implemented on a plant import sector basis, as only four sectors account for 86% of alien plant introductions, largely through one entry point. The baseline inventory and analysis will shape future management and policy directions for alien plants in Bhutan.

We examine the problem of sub-micron aluminium drop combustion when both O diffusion and Al diffusion occur. During the unsteady evolution of the combustion field the oxide that is generated has the form of a shell whose inner surface encloses an aluminium bath and whose outer surface is exposed to an air bath. The diffusing atoms can react at these surface baths and also, in principle, between themselves in the interior of the oxide. However, the mass concentrations of the atoms are small so that the interior collisions necessary for this reaction are negligible.With this important simplification we are able to define a model that leads to an analytical discussion. For small Damkohler numbers (of which there are two, one defined by the O atoms the other by the Al atoms) the relative values of the bath reaction rates determine the proportion of oxide accretion on the outer surface to accretion on the inner surface. For large Damkohler numbers the relative values of the diffusion coefficients play the same...

We pose the following question: ‘Within the context of the classical shrinking-core model for sub-micron aluminium combustion, allowing only for the diffusion of atomic oxygen (no aluminium diffusion), but with two non-classical ingredients (large Knudsen number heat losses to the ambient atmosphere and a fractal reacting surface), are the solutions consistent with four experimental facts and data sets: (i) burn times; (ii) particle temperatures; (iii) maximum temperatures independent of particle size for small Damkohler numbers; and (iv) also for small Damkohler numbers a burn law of the form d1 − ν–t (where d is the particle diameter and ν ∼ 0.7 or so)?’ In the analysis we first consider a non-fractal model and scale the lengths with (where is the diffusion coefficient and k is the reaction-rate constant) and time with (where ρ− is the aluminium density and co is a characteristic value of the O density within the alumina). Burn times are calculated which follow a linear d–t law for small values of kL/D(...

We revisit the shrinking-core model of sub-micron aluminum combustion with particular attention to the mass flux balance at the reaction front which necessarily leads to a displacement velocity of the alumina shell surrounding the liquid aluminum. For the planar problem this displacement simply leads to an equal displacement of the entire alumina layer, and therefore a straightforward mathematical framework can be constructed. In this way we are able to construct a single curve which defines the burn time for arbitrary values of the diffusion coefficient of O atoms, the reaction rate, the characteristic length of the combustion field, and the O atom mass concentration within the alumina provided that it is much smaller than the aluminum density. This demonstrates a transition between a ‘d 2–t’ law for fast chemistry and a ‘d–t’ law for slow chemistry. For the spherical geometry, the one of physical interest, the outward displacement velocity creates not a simple displacement, but a stress field which, wh...

A computational framework is developed to investigate nozzle erosion in solid-propellant rocket motors. The calculations have several novel features. Among these is an accounting of three-dimensional effects, most strikingly for a vectorednozzle but also in thedescription of the turbulentflow.Also, instead of the hitherto universal strategy of merely solving the nozzle flow with uniform inlet conditions, strategies by which the chamber flow with its nonuniform efflux can be coupled to the nozzle flowwhile still resolving the nozzle boundary layer are discussed. The chamber flow is approximated by either full motor simulations, which do not resolve the boundary layer, or by an asymptotic strategy valid for slender chambers: one first used in turbulent boundary-layer studies. The manner in which the chamber efflux conditions are used as nozzle inlet conditions is part of the discussion. The results suggest that specifying turbulent rather than uniform inlet conditions can have a significant effect on nozzle erosion.

Non-uniform methane diffusion flames, formed from a porous plug burner spinning in quiescent air, are investigated numerically in a three-dimensional context. Flames are simulated for Damkohler numbers on the upper branch of the S-shaped response curve close to the extinction point. Multi-dimensional instabilities appear in the form of holes and spirals at these near extinction Damkohler numbers, as observed in experimental studies of flames sustained by a rotating porous burner [V. Nayagam, F.A. Williams, Pattern Formation in Diffusion Flames Embedded in Von Karman Swirling Flows , NASA/CP 2001-21082; V. Nayagam, F.A. Williams, Pattern Formation in Diffusion Flames Embedded in Von Karman Swirling Flows , NASA/CR 2006-214057]. Simulation results from the constant density and constant viscosity model suggest that the non-uniform flames are a result of thermo-diffusional instabilities and are a function of the Damkohler number. The simulated flame holes have stationary edges while the single and double spirals have edges that rotate about the axis of the burner. It is found that boundary conditions such as the mixture strength and the injection velocity affect the range of Damkohler numbers within which the system is unstable.

Flame ball interactions are numerically investigated in a reaction–diffusion system characterized by single-step Arrhenius kinetics and radiative heat losses. It is found that the interactions of two neighbouring flame balls are characterized by two distinct regimes – a repulsion regime and an attraction regime, depending upon the separation distance. The two regimes join at a critical separation distance, which corresponds to an unstable equilibrium state. For supercritical separation distances, the two flame balls repel and drift apart from each other; whereas for sub-critical separation distances, they move towards each other and eventually merge into a single stationary flame ball. In this connection, flame ball interactions are found to exhibit a qualitatively reverse character in comparison with the well-known van der Waals curve which characterizes intermolecular forces.

As a doctor, at any stage of your training, you may in the course of your work, and sometimes outside it, be called upon to administer resuscitation to either a patient or another person. All general practitioner's (GP) practices should have a defibrillator, and defibrillators are often available in public places such as stations and supermarkets. The Quality and Outcomes Framework rewards practices for regularly updating cardiopulmonary resuscitation (CPR) skills of practice clinical and non-clinical staff (education indicators 1 and 5). In addition, all members of the public should be encouraged to consider taking the basic training as the earlier cardiopulmonary resuscitation is initiated after a collapse, the more likely it is to succeed.

In this paper, we present a set of computational simulations of the deflagration of composite propellants comprising octogen and hydroxyl-terminated polybutadiene. The focus of the investigation is on the parameter calibration of simplified global kinetics models used to determine gas-phase chemical rates. The calibration is based on a collection of experimentally measured burning characteristics for pseudopropellants comprising octogen and hydroxyl-terminated polybutadiene with different solid loadings and uses exclusively homogeneous, one-dimensional, steady burning information. The task of including a large set of burning characteristics is accomplished by transforming the calibration into an optimization problem that is solved by means of a genetic algorithm. Models of increasing accuracy are constructed by enlarging the set of matched performance and the parameter space. The objective is to demonstrate the influence of the calibration of such models on three-dimensional simulations in which the size of the oxidizer particles is not neglected. A quantitative comparison of prediction and experiments is presented.

A numerical description of heterogeneous propellant combustion enables us to examine the spatial and temporal fluctuations in the flow field arising from the heterogeneity. Particular focus is placed on the fluctuations in a zone intermediate between the combustion field (where reaction is important) and the chamber flow domain, for these define boundary conditions for simulations of the turbulent chamber flow. The statistics of the temperature field and the normal velocity field are described, and characteristic length scales and time scales are identified. The length scales are small compared to any relevant length scale of the chamber flow, and so the boundary conditions for this flow at any mesh point are statistically independent of those at any other mesh point. But the temporal correlations at a fixed point are significant, and affect the nature of the chamber flow in a variety of ways. We describe the fluctuations in the head-end pressure that arise because of them, and contrast these results with those calculated using a white-noise assumption.

In the study of heterogeneous propellants that contain large amounts of fine aluminum and ammonium perchlorate, it is appropriate to distinguish between the matrix (a homogenized blend of fine particles and binder) and larger particles that are embedded in this matrix. Then the burning properties of a pure matrix are required. We construct a one-dimensional model for this purpose. Key ingredients include the determination of the thermal conductivity and pyrolyis law of the matrix, and an accounting of the radiation field generated by the fine aluminum in the gas phase. Experimental results of Dokhan et al. ("The Ignition of Ultra-Fine Aluminum in Ammonium Perchlorate Solid Propellant Flames," AIAA Paper 2003-4810, July 2003) are used for calibration and in comparisons.

We examine an axi-symmetric deflagration located in a tube with thermally active walls. It is noted that the flame-in-tube configuration defines a classical edge-flame, a flame in a shear flow for which there is a water-shed solution for a critical value of the Damkohler number ( D ), ignition front solutions for larger values of D , and failure wave solutions for smaller values. We examine semi-infinite tubes with a heat flux imposed at the tube wall ends, to simulate experiments reported in the 30th Symposium. We identify parameters for which stable solutions are obtained at certain flow rates, but unstable solutions are generated at higher flow rates, followed by stable solutions at still higher flow rates. These solutions are consistent with the experimental record. Instability leads either to regular oscillations or to a violent process characterized by quenching and re-ignition.

Our simulations of heterogeneous propellant combustion have always assumed that the oxidizer particles (ammonium perchlorate) are disks (two dimensional) or spheres (three dimensional). Here the effects on the burning rate are examined when the disks/spheres are replaced by ellipses/ellipsoids. In two dimensions, it is shown that an area-preserving deformation of a pack of disks, generating a pack of ellipses, can lead to significant variations in the burning rate. However, if the ellipses are randomly packed, so that the alignment of their axes is random, the shape effect is small. In three dimensions, volume-preserving deformation, which generates ellipsoids, leads to burning rate changes no greater than those in two dimensions. Absent a random packing algorithm for ellipsoids, it is speculated that here also a random alignment of the axes would eliminate the effect. ECENT years have seen significant advances in the modeling of heterogeneous propellant combustion, specifically in the context of ammonium‐perchlorate (AP)/hydroxyl-terminatedpolybutadiene propellants. In Ref. 1, a two-dimensional treatment, a numerical code is described in which the combustion field is fully coupled to heat conduction in the solid via a nonuniformly regressing nonplanar surface. The corresponding three-dimensional problem is described in Refs. 2 and 3, the first using two-step kinetics and the second three-step kinetics. Comparisons between the numerical results and experimental results of Miller 4 show that the effects of propellant morphology on burning rates can be satisfactorily predicted over a wide pressure range. At fixed pressure, the variations in burning rate due to different morphologies are as much as threefold, so that these are nontrivial predictions. In this connection, note how we chose the values of the numerous parameters for this problem, parameters identified in Refs. 1‐3. Most are typical values defined by the community at large. Some are uncertain, of course, particularly the surface pyrolysis parameters, but once a choice was made no post hoc adjustments were made to better fit the three-dimensional data of Miller. An important parameter subset is those of the gas kinetics, the reaction rates for the two-step and three-step kinetics. There, we used one-dimensional burning rate data for pure AP and for homogeneous blends of AP and binder. The use of a three-step mechanism enabled us to fit blend burning rates over a wide range of mixture ratios, and it is presumably for this reason that the three-step results are more accurate than the two-step results. Most important, our calculations are not a massive exercise in curve fitting. This does not mean that better choices for some of our parameter values are not possible. Although we reasonably capture qualitative aspects of sandwich burning, 3 most notably the surface topography, the surface topography in our three-dimensional simulations does not show concavity in the surfaces of large AP particles at pressures for which it is observed experimentally. It seems probable that this

We use numerical strategies to examine the stability of reverse smolder waves in the context of a model that can permit both fuel-rich and fuel-lean waves. The steady-state response for such waves, maximum temperature versus blowing rate, is characterized, for increasing blowing rate, by a fuel-rich branch of rising temperature followed by a fuel-lean branch of falling temperature, followed by quenching. The propagation speed at the quenching point is non-zero. For the parameters that we consider, the entire fuel-rich branch is unstable to two-dimensional disturbances, but the dynamic consequences are modest. An interval of the fuel-lean branch whose left boundary is at the point of stoichiometry is stable, but the remainder of the branch, all the way to the quenching point, is unstable. These instabilities are destructive, and the smolder wave becomes fragmented. Tribrachial fragments can emerge, analogous to the tribrachial or triple flames familiar from gaseous edge-flame studies. Their emergence is ch...

Random packs of ammonium perchlorate and aluminum particles in fuel binder, of the kind used to mimic the morphology of heterogeneous propellants, define distributions of aluminum particles that can be used as the starting point of agglomeration studies. The goal is to predict the fraction of aluminum that agglomerates and the size distribution of the agglomerates. Three phenomenological models are described, each with one or two parameters that can be adjusted to fit experimental data, and a number of such fits are attempted. It is shown that the agglomeration models can be calibrated to match a wide variety of propellant outputs, as needed for the numerical simulation of rocket chamber flows with aluminum injection. Results for such flows are presented and provide information about the distribution of the aluminum droplets and of the alumina smoke particles that arise from its presence.

A numerical code for the simulation of heterogeneous propellant burning is used to examine the response to the pressure field of an incident acoustic wave. It is shown that there are two natural response functions, one defined by the perturbation mass flux beyond the combustion field, the other by the perturbation energy flux beyond the combustion field. The first of these plays an essential role in L * instability (a coupled propellant–rocket-chamber phenomenon), and the second in whether the acoustic wave is amplified on reflection (a phenomenon exclusive to the propellant). We show, for several choices of parameter values and propellant morphology, that the two responses are qualitatively similar, albeit they differ in magnitude by modest amounts. We show that in some cases each response displays a single maximum or peak as a function of frequency, in other cases multiple peaks are obtained. A tentative hypothesis is proposed as a predictor of multiple peaks.

We examine the evolution of reverse smolder waves with edges, motivated by the existing literature on edge-flames. An advancing smolder edge proves to be of little interest, and a well-defined invariant structure does not emerge following initial transients. A retreating smolder edge also lacks invariant structure, but retreats at a reasonably well-defined speed and can lead to novel structures and novel evolutions. Thus, a transient propagating smolder spot can be generated; and a tribrachial structure evolves from this spot with a tail that has the form of a forward smolder wave, and two leading branches, fuel-lean and fuel-rich reverse smolder waves. High temperatures and high reaction rates accompany these evolutions, and it is noted that this could lead to flaming (gas-phase) combustion.

We examine edge-flames in the context of symmetric counterflows of fresh mixture, and examine their dynamics when the rate of strain is varied periodically in time. For a Lewis number of 1, extinction boundaries and zero (in the mean) edge propagation speed boundaries are constructed in the forcing amplitude—Damkohler number plane. Forcing can turn advancing edges into retreating edges. For a Lewis number of 0.3, the fundamental distinction is between flames that display cellular structures and flames that do not. Forcing can convert a non-cellular flame into one with cells; and it can strongly affect the dynamics of cellular structures that exist in the absence of forcing.

A two-dimensional numerical model is developed to simulate combustion and heat transfer in ‘Swiss roll’ combustors (SRC). This model couples heat transfer and chemical reaction in the gas and heat diffusion in the conducting walls. The goal of the model is to gain insight into micro-scale combustion to prevent the occurrence of extinction. In the numerical modelling, the ‘Swiss roll’ geometry is unwrapped into a straight channel, with heat recirculation between the unburnt and burnt gas being appropriately taken into account. The simulation is carried out using a fourth-order scheme to discretize the spatial variables, with time integration to steady state, based on a first-order Runge–Kutta scheme. We investigate the extinction mechanisms and heat transfer characteristics in the combustor, and perform parametric studies to examine their effects on combustion and extinction. Numerical predictions of extinction limits agree well with experimental data.

We discuss the manner in which one-dimensional unsteady descriptions can be constructed from multidimensional unsteady simulations of heterogeneous propellant combustion. Spatial averaging of the heat equation within the propellant is used to generate a one-dimensional equation with a number of source terms defined by the multidimensional thermal field and surface corrugations. Each of these terms is evaluated numerically, and those that can be neglected are identified; models are defined and tested for those that cannot. Closure of the one-dimensional description is achieved by relating the mean surface regression rate and the heat flux from the combustion field at the surface to the pressure and the average surface temperature. These relations are in the form of a look-up table generated from the “exact” (multidimensional) simulations. The accuracy of the one-dimensional system is tested by comparing the predictions with those of the exact model. This is done for steady burning rates at various pressures and for the unsteady burning response to pressure ramps and pressure pulses.

We examine sandwich propellants constructed from sheets of pure ammonium perchlorate (AP) interleaved with an AP/binder blend, and construct solutions numerically using a code that fully couples gas-phase and solid-phase processes via an unsteady moving interface. This code has been used elsewhere to simulate the burning of random packs of spherical AP particles embedded in binder. We show that for a stoichiometric configuration, variations of the burning rate with α (a measure of the oxygenation of the AP/binder blend) are not monotonic, but display a weak maximum; and variations of the burning rate with sandwich thickness are monotonic for small α, but display a minimum for large α (e.g. α = 0.5). When the equivalence ratio is varied, the burning rate displays a maximum on the fuel-lean side when α is small, on the fuel-rich side when α is large. These results, and the manner in which the sandwich topography varies with the different parameters, suggest that the configuration could be invaluable for val...

Inearlierworkithasbeenshownthatspheresofvarioussizescanberandomlypackedtosimulatethemorphology ofammoniumperchlorate (AP)/binderheterogeneouspropellants.Amodelisnowformulated in whichpropellants dee nedinthiswaycanbeburnt,allowingforcompletecouplingbetweenthegas-phasephysics,thecondensed-phase physics, and the unsteady nonuniform regression of the propellant surface. The gas-phase kinetics is represented by a two-step model with parameters e tted to experimental data for the one-dimensional combustion of pure AP and the one-dimensional combustion of a e ne-AP/binder blend. In the discussion of the pure AP e ts, the issue of intrinsic instabilities arises, and these are explored using nonlinear direct numerical simulation and a numerical linear-stability strategy. Results for two-dimensional heterogeneous burning show that surface regions where the AP and binder can mix regress more rapidly than those dominated by AP; local extinction can occur where the binder dominates. Time variations in the integrated e ux-based equivalence ratio are shown to be large. Variations in the average burning rate with pressure are consistent with the (three-dimensional ) experimental record. Nomenclature cp = specie c heat D1;2 = reaction rate constants dj = diameter of the jth particle class E = activation energy f = surface function M = mass e ux Nj = number in the jth particle class n1;2 = pressure exponents in the reaction rates

A numerical framework is described which permits the calculation of the three-dimensional combustion field supported by a heterogeneous propellant, allowing for complete coupling between the condensed-phase physics, the gas-phase physics, and the unsteady uneven, regressing surface. A random-packing algorithm is used to construct models of ammonium perchlorate (AP) in hydroxyl-terminated polybutadiene propellants which minic experimental propellants designed by R. Miller, and these are numerically burnt, Mean burning rates are compared with experimental data for four packs, over a pressure range of 7–200 atm. The effect of the local propellant morphology on the local surface regression speed is examined, with particular attention to the behavior in the neighborhood of large AP particles, At first, these burn slowly and protrude significantly above the surrounding surface, but later they are rapidly consumed and the surface flattens. In all cases, mean burning rates can be accurately calculated using an Oseen approximation for the velocity field, rather than solving the Navier-Stokes equations.

We examine random packs of discs or spheres, models for ammonium-perchlorate-in-binderpropellants, and discuss their average properties. An analytical strategy is described for calculating the mean or effective heat conduction coefficient in terms of the heat conduction coefficients of the individual components, and the results are verified by comparison with those of direct numerical simulations (DNS) for both two-dimensional (disc) and three-dimensional (sphere) packs across which a temperature difference is applied. Similarly, when the surface regression speed of each component is related to the surface temperature via a simple Arrhenius law, an analytical strategy is developed for calculating an effective Arrhenius law for the combination, and these results are verified using DNS in which a uniform heat flux is applied to the pack surface, causing it to regress. These results are needed for homogenization strategies necessary for fully integrated two- or three-dimensional simulations of heterogeneous propellant combustion, and some sample two-dimensional results are presented.

We examine anchored edge-flames in non-premixed combustion for which the Lewis number of the fuel is large. Steady two-dimensional solutions are constructed, both stable and unstable, by using a modified time-integration strategy. These calculations define a static detachment Damkohler number. Real-time integrations reveal oscillating instabilities if the Damkohler number D is small enough, and these instabilities are also examined by linear perturbation of the steady solutions. The eigenfunctions constructed in this way make clear that the instability is confined to the edge, and does not affect the 1D flame trailing from the edge. Dynamic detach-ment of an oscillating flame occurs in one of two ways, depending on the boundary conditions used in the model: as D is decreased, the period and amplitude of the oscillation grow and approach infinity as D approaches a critical value greater than the static detachment value; or, the period and amplitude remain bounded, and dynamic detachment occurs at the same value of D as for static detachment.

It isshown thatrandom packsofspheresofvarioussizescan beconstructed thatmodelammonium ‐perchloratein-binder propellants in thesense that both thesize distributions and thepacking fractions of industrial propellant packs can be matched. Strategies for dealing with fractional numbers of large particles are addressed, as are strategies for dealing with a large number of very e ne particles (e ne powder). Fine powder is necessary in a threedimensional pack to achieve the required stoichiometric ratio of ammonium perchlorate to fuel binder, but is not necessary in a two-dimensional (disk) pack. Some preliminary calculations of the two-dimensional combustion e eld supported by a disk pack are presented, in which full coupling between the gas phase, the condensed phase, and the retreating nonplanar propellant surface is accounted for. Nomenclature D1;2 = reaction rate constants dj = mean diameter of particles E1;2 = activation energies L = length of a pack edge N = total number of particles Nj = number of particles in the jth class n j = number fraction of particles in the jth diameter classs n1;2 = pressure exponents Ru = universal gas constant R1;2 = reaction rates rb = surface regression rate T = temperature Vj = volume of particles in the jth class v j = volume fraction of particles in the jth class X = mass fraction of ammonium perchlorate (AP) Y = mass fraction of fuel binder Z = mass fraction of AP decomposition products ´ = surface function A = surface location A = level set function dee ning the pack

We discuss edge-flames in the context of the plane counterflow of air and nitrogen-diluted hydrogen. For sufficiently dilute hydrogen streams, strong cellular instabilities arise which affect the dynamics of the edge-flames and, in the long term, give rise to residual cellular structures. Depending on the Damkohler number, solutions are constructed corresponding to: an advancing edge trailing a smooth flame; an advancing edge trailing a stationary periodic cellular structure, a warp of flame-strings; a finite array of flame-strings which drift apart from each other at a decreasing rate; a single stationary flame-string; dual stationary flame-strings; triple stationary flame-strings. Many of these solutions are sublimit in the sense that they exist for Damkohler numbers smaller than the one-dimensional quenching value defined for the counterflow configuration. The connection of these solutions to the linear stability of the one-dimensional system is discussed, and evidence of a subcritical bifurcation is presented. Comparisons are made with experimental results obtained by Ronney.

We develop a mathematical model that describes the unsteady burning of a heterogeneous propellant by simultaneously solving the combustion field in the gas-phase and the thermal field in the solid-phase, with appropriate jump conditions across the gas/solid interface. The model takes into account the ammonium perchlorate (AP) decomposition flame, reaction between the AP products and the binder gases, different properties (density, conductivity) of the AP and binder, temperature-dependent, gas-phase transport properties, and the unsteady nonplanar regressing surface. Propagation of the latter is described by using a level-set formulation which gives rise to a Hamilton–Jacobi equation. Numerical studies for a periodic sandwich geometry show that the surface evolves unsteadily into a steadily propagating front, and the effects of various parameters (pressure, stoichiometry, length scale) on the steady propagation speed are discussed. A variety of surface shapes are predicted, depending on the parameter values. It is shown that accounting for the full Navier–Stokes equation in the gas phase yields results that differ little from those generated when an Oseen model is adopted.

We construct the combustion e eld generated by a periodic reactant supply that models the supply from a heterogeneous propellant. A full accounting of the e uid mechanics is incorporated. However, solutions differ little from those generated asssuming a uniform mass e ux (theconstant density model ). On the other hand, allowing for temperature-dependent transport (power law or Sutherland’ s law ) strongly affects the reaction rate and the heat e ux to the propellant surface. The effects of nonuniform mass e ux at the propellant surface are discussed, such nonuniformity arising, for example, because of the different densities of the oxidizer and binder. And we discuss the effects of hills and valleys in the propellant surface.

We examine small deviations from axial symmetry in a solid-propellant rocket motor, and describe a ‘bath-tub-vortex’ effect, in which substantial axial vorticity is generated in a neighbourhood of the chamber centreline. The unperturbed flow field is essentially inviscid at modest Reynolds numbers, even at the chamber walls, as has long been known, but the inviscid perturbed flow is singular at the centreline, and viscous terms are required to regularize it. We examine perturbations sufficiently small that a linear analysis is valid everywhere (εRe small, where ε is a measure of the perturbation amplitude and Re is a Reynolds number), and larger perturbations in which a nonlinear patch is created near the centreline of radius O(√ε). Our results provide an explanation of swirl experimentally observed by others, and a cautionary note for those concerned with numerical simulations of these flows, whether laminar or turbulent.

We examine a simple model of a side-anchored non-premixed edge-flame in order to gain insights into the oscillations that are sometimes observed in microgravity candle burning, flame-spread over liquids, etc. Previous results describe the role played by the Lewis number of the fuel, and the Damkohler number, and here we examine both the effects of an on-edge and off-edge convective flow, and the effects of a heat sink. The on-edge flow and the heat sink tend to destabilize and the off-edge flow tends to stabilize, results consistent with our hypothesis regarding the genesis of the oscillations.

The complex combustion Ž eld that is generated by burning a heterogeneous solid propellant of the kind used in high-performance rockets is studied. We consider a propellant whose surface is one-dimensional periodic, generating a two-dimensional combustion Ž eld. Two important parameters are the Peclet number Pe and the solid-phase stoichiometric coefŽ cient . We show that for = 7, a representative value, there are essentially two  ame conŽ gurations: For small Peclet numbers, mixing between the surface and the  ame is sufŽ cient to generate a continuous and near-uniform de agration; for Peclet numbers of order 10 or so, each period contains a pair of buttonlike premixed  ames centered over the fuel so that there are signiŽ cant holes in the combustion Ž eld over the oxidizer. Diffusion- ame structures that are part of the combustion Ž eld play no role in generating the heat that is conducted back to the propellant surface. Most of our calculations assume that both Lewis numbers are equal to 1 and that the solutions are steady, but time-periodic oscillating solutions are obtained for sufŽ ciently large values of Lewis number.

We examine a single diffusion flame anchored to 1/4-spaces of solid fuel and oxidizer, a configuration relevant to the combustion of heterogeneous solid propellants. A time-periodic shear flow is applied, to model the shear that can be generated by the interaction of acoustic waves and the rotational base flow in a rocket chamber. The response of the flame to this shear, the heat flux to the surface, etc., are calculated numerically. Significant enhancement of the maximum temperature and the time-averaged total heat flux to the surface are found. These enhancements are essentially maximized at zero frequency, and at low frequencies the response depends critically on the instantaneous direction of the shear.

We examine a surface which mimics that of a heterogeneous propellant and through which passes distributed fluxes of oxidizer and fuel. The three-dimensional flames supported by these fluxes we calculated using a simple model. An elementary propellant packing model defines a variety of flux distributions according to the level of the slice through the propellant which defines the surface, and the effect of the different distributions on the combustion field and on the heat flux to the surface is discussed. An important geometric effect is identified. The more likely that arbitrary surface area fractions contain both ammonium perchlorate (AI) and binder fluxes, the greater will be the total heat flux to the surface from the AP/binder flames. The likelihood, and therefore the heat flux, is maximized for fuel-rich slices. This work is part of an ongoing study whose goal is a sophisticated numerical model of three-dimensional heterogeneous propellant burning.

We examine the geometry of diffusion flames generated by the burning of a heterogeneous solid propellant, using a simple model designed to provide qualitative insights. In the fast chemistry limit a strategy is used which has its roots in Burke and Schumann’s 1928 study of diffusion flames, albeit with different boundary conditions. This shows that the stoichiometric level surface (SLS) intersects the propellant surface at a point displaced from the fuel/oxidizer interface, and the variations of this displacement with Peclet number are discussed. We show that for model sandwich propellants, or their axisymmetric counterpart, the geometry of the SLS when the core is oxidizer is quite different from the geometry of the SLS when the core is fuel. Also, it is much easier to quench the flame on an oxidizer core, by reducing the Peclet number, than it is to quench the flame on a fuel core. When finite chemistry effects are accounted for, the flame only occupies a portion of the SLS, and there is a leading edge structure in which premixing plays a role. Enhancement of the burning rate due to premixing is identified, but a well-defined tribrachial structure is not observed. We show how a sharp reduction in pressure can lead to a detachment of the flame from the SLS, with subsequent quenching as it is swept downstream.

We examine twin premixed flames in a plane counterflow and uncover, in the parameter space, a hitherto unknown domain of cellular instability. This leads us to hypothesize that for small Lewis numbers a two-dimensional (2D) steady solution branch bifurcates from the one-dimensional (1D) solution branch at a neutral stability point located near the strain-induced quenching point. Solutions on this 2D branch are constructed indirectly by solving an initial-value problem in the edge-flame context defined by the multiple-valued bistable 1D solution. Three kinds of solution are found: a periodic array of flame-strings, a single isolated flame-string and a pair of interacting flame-strings. These structures can exist for values of strain greater than the 1D quenching value, corresponding to sublimit solutions.

We examine a premixed flame located in a plane counterflow of fresh cold mixture and hot inert. The temperature of the inert is significantly less than the adiabatic flame temperature, so that the flame response to strain-rate variations is multivalued for a finite interval of strain rates. In this interval there are two stable one-dimensional solutions, one characterized by vigorous combustion, the other by weak combustion. Numerical solutions are constructed that describe an unsteady two-dimensional evolution between the two solutions in the direction normal to the straining-flow plane. Following an initial transient, this evolution consists of a wave of permanent form, traveling at constant speed in the out-of-plane direction. This wave is an edge-flame whose speed is positive or negative, depending on the value of the strain rate. The role of edge-flames in the failure of upward rising methane/air flames in sublimit mixtures is briefly discussed.

This paper is a continuation of our work on edge-flames in premixed combustion. An edge-flame is a two-dimensional structure constructed from a one-dimensional configuration that has two stable solutions (bistable equilibrium). Edge-flames can display wavelike behavior, advancing as ignition fronts or retreating as failure waves. Here we consider two one-dimensional configurations: twin deflagrations in a straining flow generated by the counterflow of fresh streams of mixture: and a single deflagration subject to radiation losses. The edge-flames constructed from the first configuration have positive or negative speeds, according to the value of the strain rate. But our numerical solutions strongly suggest that only positive speeds (corresponding to ignition fronts) can exist for the second configuration. We show that this phenomenon can also occur in diffusion flames when the Lewis numbers are small. And we discuss the asymptotics of the one-dimensional twin deflagration configuration. an overlooked problem from the 70s.

For a one-component reaction model, the total diffusive heat flux (TDHF) is—∇(λT+pDQY) where λ and pD are diffusive transport coefficients, T is the temperature, Y is the reactant mass-fraction, and Q is the heat of reaction. We show that a flame ball exposed to a weak TDHF will drift, and we derive an explicit formula for the drift speed. The key mathematical feature is that the flux generates a flametemperature perturbation that varies as cosφ, where φ is the polar angle measured from the axis parallel to the flux vector, and this is unacceptable as it leads to a simple boundary-value problem for a harmonic function (a temperature perturbation) that has no solution. Drift generates a like perturbation and the drift speed must be chosen so that the two cancel. If the TDHF is generated by a second flame ball whose far-temperature-field is suppressed by radiation, so that only ∇Y contributes to the flux, the balls will drift apart with a separation distance that grows as the one-third power of time. Observations made during recent space shuttle flights are presented and are consistent with this prediction. We also formulate the problem of drift in a weak gravitational field and solve it in an approximate fashion.

We describe an elementary model of one-dimensional unsteady forward smoldering, purged of all unnecessary physics. Following work of Dosanjh and Pagni, a late time solution is constructed, characterized by two reaction fronts—an exothermic oxidation front, an unusual kind of diffusion flame; and an endothermic pyrolysis front. It is shown that the flame temperature and the ratio of the speeds of the two fronts relative to the solid are independent of the blowing rate, in agreement with data obtained by Ohlemiller and Lucca. The structure of the oxidation front is described in the context of one-step Arrhenius kinetics, and it is shown that leakage of solid reactant through the front is possible, but not leakage of oxygen. An elementary pyrolysis structure is also examined which reduces to the frontal model in a certain limit, and clarifies its nature.

Fast-time instabilities refer to dynamics that may develop within the reaction zone of a flame, where the chemical kinetic time scales are very brief. Premixed flames with order one heat losses and diffusion flames with order one reactant leakage are known to possess this instability when the Lewis number is one (Peters, 1978). Work by Stewart (1986) indicates that the instability should also arise for adiabatic flames with Lewis numbers exceeding one. Recent work in reverse smouldering combustion (Lozinski and Buckmaster, 1994) requires an examination of the combined effect of heat losses and Lewis numbers well below unity. Because of the general nature of the results, they are presented here. The numerical computations reveal that while heat losses tend to destabilize the flame, small Lewis numbers have a countervailing stabilizing effect, suppressing the instability for an order one range of heat losses. This plays a key role in selecting the physically significant solution to the reverse smou...

A simple model of reverse smolder in a porous medium is analyzed using asymptotic methods. When the only chemical reaction is exothermic oxidation, the burning rate is a single-valued function of the blowing rate, increasing from zero to a maximum, and then returning to zero. When endothermic pyrolysis is added to the description, the burning rate is double-valued for blowing rate less than some maximum. Beyond this maximum there are no solutions. The upper branch of the double-valued solution is the physically relevant one. On it, for certain choices of parameters, the burning rate increases from zero to a maximum, and then decreases until quenching occurs at the maximum blowing rate. This behavior mimics experimental observations by Torero, Fernandez-Pello, and Kitano [15].

We examine the stability of premixed flames in mixtures containing significant amounts of fine inert dust whose sole impact is upon the radiative transport. By using well-established modeling strategies together with a simple radiation model which preserves much of the essential physics, it is possible to explore to what extent radiative transport displaces the classical non-hydrodynamical stability boundaries of the plane deflagration. Analysis is possible for arbitrary values of both the Planck length and the Boltzman number. It is shown that the pulsating/traveling-wave instability is strongly enhanced by the presence of radiation, and can be present even if Le < 1. On the other hand, radiation tends to suppress the cellular instability normally associated with values of Le less than 1. The latter is consistent with preliminary experimental observations of Abbud-Madrid and Ronney.

We examine an expanding spherical premixed flame propagating in a mixture containing inert dust. The presence of the dust generates a significant radiative energy flux that influences the flame speed. With the adoption of a hydrodynamic description in which stretch effects are accounted for using an empirical formula, and with the use of the Eddington approximation to describe the radiation, a simple numerical problem is formulated valid for that initial time interval in which the flame-temperature changes by O(e) amounts where c is the small inverse activation energy. Solutions are constructed using parameter values appropriate to lean CH^/air mixtures, and for modest particle loadings. We describe the competition between the Zeldouich-Spalding effect in which radiative losses on the diffusive scale tend to quench the flame, and the Joulin effect in which radiative preheating on the scale of the Planck length tends to strengthen the flame.

The authors examine flame balls that are not optically thin so that radiation from the hot burned gas is not lost but is reabsorbed by the surrounding cool gas. The steady solution is shown to be multivalued in general and defines an intrinsic (apparatus independent) flammability limit for a sufficiently small ignition source. Beyond the flammability limit a steady solution exists for arbitrarily weak mixtures, but is unrealizable since it is unstable to one-dimensional perturbations. An unsteady propagating flame solution is also possible for arbitrarily weak mixtures, but can only be generated by a large ignition source. Observations of flame-strings in SF[sub 6]-diluted mixtures are reported and suggest that the peculiar nature of the radiative properties of SF[sub 6] is responsible for peculiar dynamics.