Extended combustion model for single boron particles - Part I: Theory

Ramjet engines have significant advantages when compared to conventional rocket motors concerning specific impulse, manoeuvrability, and range. Boron particle addition to the propellant of ducted rockets further increases this potential due to a very high heating value. However, the combustion of boron particles is a very complex process because of an inhibiting oxide layer covering the particles. This layer has to be removed before vigorous combustion can start. The boron particle combustion process runs in two distinct stages. In the literature review presented in this article two combustion models for single boron particles are outstanding. A very detailed model by the Princeton/Aerodyne group features hundreds of elementary reactions and considers all physical processes in the particle environment. It is very elaborate and, thus, not suitable for incorporation into three-dimensional CFD-calculations at present. The second model developed at Penn State University takes on a global approach with only a few reactions which makes it promising for CFD applications. A careful analysis of this model revealed some inconsistencies, errors and drawbacks which gave rise to the new model presented in this paper. The new model comprises a consistent formulation of the heat and mass transfer processes in the particle environment based on a quasi-steady approach, accounts for boron evaporation which is a relevant process despite the high boiling point of boron, and it considers the influence of forced convection on the particle conversion. The chemical reaction rates adopted from the original model were revised and are slightly changed, the differential equations to be solved are corrected and an iterative solution algorithm is introduced. A careful validation of the model is presented in Part II of this paper showing that the new model is suitable for boron particle sizes relevant for ramjet combustion chambers.     

Extended combustion model for single boron particles - Part II: Validation

Boron particle addition to propellants is advantageous due to a very high heating value. However, the combustion of boron particles is a very complex process because of an inhibiting oxide layer covering the particles. This layer has to be removed before vigorous combustion can start. Hence, the boron particle combustion process runs in two distinct stages. There are two outstanding combustion models for single boron particles in the literature. A very detailed model by the Princeton/Aerodyne-group features hundreds of elementary reactions and considers all physical processes in the particle environment. The second model developed at Penn State University takes on a global approach with only a few reactions which makes it promising for CFD applications. A careful analysis of this model revealed some inconsistencies, errors and drawbacks which gave rise to the new model presented in Part I of this paper. The new model comprises a consistent formulation of the heat and mass transfer processes in the particle environment based on a quasi-steady approach, accounts for boron evaporation which is a relevant process despite the high boiling point of boron, and it considers the influence of forced convection on the particle conversion. The chemical reaction rates adopted from the original model were revised and are slightly changed, the differential equations to be solved are corrected and an iterative solution algorithm was introduced. In Part II, the results of the new extended model are compared to experimental data from literature and opposed to results of the other two models. They show reasonable agreement with measured data. A more complex transient model is also derived which serves as a means of scrutinising the principal assumption of the new model which are quasi-steady state changes. It appears that the new model is suitable for boron particle sizes relevant for ramjet combustion chambers.     

Ignition transition in turbulent premixed combustion

Recently, Shy and his co-workers reported a turbulent ignition transition based on measurements of minimum ignition energies (MIE) of lean premixed turbulent methane combustion in a centrally-ignited, fan-stirred cruciform burner capable of generating intense isotropic turbulence. Using the same methodology, this paper presents new complete MIE data sets for stoichiometric and rich cases at three different equivalence ratios ? = 1.0, 1.2 and 1.3, each covering a wide range of a turbulent Karlovitz number (Ka) indicating a time ratio between chemical reaction and turbulence. Thus, ignition transition in premixed turbulent combustion depending on both Ka and ? can be identified for the first time. It is found that there are two distinct modes on ignition in randomly stirred methane–air mixtures (ignition transition) separated by a critical Ka where values of Ka_c ≈ 8–26 depending on ? with the minimum Ka_c occurring near ? = 1. For Ka < Ka_c, MIE increases gradually with Ka, flame kernel formation is similar to laminar ignition remaining a torus, and 2D laser tomography images of subsequent outwardly-propagating turbulent flames show sharp fronts. For Ka > Ka_c, MIE increases abruptly with Ka, flame kernel is disrupted, and subsequent randomly-propagating turbulent flames reveal distributed-like fronts. Moreover, we introduce a reaction zone Péclet number (P_RZ) indicating the diffusivity ratio between turbulence and chemical reaction, such that the aforementioned very scattering MIE data depending on Ka and ? can be collapsed into a single curve having two drastically different increasing slopes with P_RZ which are separated by a critical P_RZ ≈ 4.5 showing ignition transition. Finally, a physical model is proposed to explain these results.     

Gas-phase combustion synthesis of particles

The current work summarizes recent experimental and theoretical investigations of the fundamental processes governing gas-phase combustion synthesis of particles. Various experimental methods and results are reviewed for the production of non-oxide, single-oxide, and mixed-oxide powders. Parameters influencing particle morphology and composition including electric field effects are discussed. Nucleation and growth models are presented for the different growth regimes, including homogeneous nucleation, agglomeration, and coalescence.     

Ignition and combustion behaviour of vegetable oils after injection in a constant volume combustion chamber

The ignition and combustion behaviour of vegetable oils to be used as fuel in combustion engines was researched using a constant volume combustion chamber. The chosen vegetable oils were characterised using the two structure indices average number of carbon atoms AC and average number of double bonds ADB. The structure indices were derived from the composition of the analysed fatty acids. The performance of these two structure indices in estimating differences in fuel properties, such as density, net calorific value, elementary composition and surface tension, was shown. The structure indices were also used to explain ignition and combustion behaviour. Differences in ignition and combustion behaviour were primarily recognised in the ignition delay and the first phase of combustion (premixed combustion). No differences were observed between the vegetable oils in subsequent phases of combustion. The longer the ignition delay, the higher the share was of premixed combustion. Models for the prediction of the ignition delay were developed using ADB. The ignition delay rises with increasing ADB. Differences in AC had no significant impact on the ignition delay. Hence, vegetable oils with a high ignition quality are characterised by a low amount of double bonds. The developed models can be used for estimation of the ignition quality and combustion behaviour of unknown vegetable oils.     

Ignition and combustion of n-heptane droplets in carbon dioxide enriched environments

The ignition process and burning characteristics of fiber-supported n-heptane fuel droplets in carbon dioxide enriched and varying pressure environments have been studied under normal gravity. Measured values of droplet burning rates, flame dimensions, broad-band radiant emission, and ignition times were compared to droplets burning in standard air conditions. The burning rate constants increased with increasing carbon dioxide concentration or pressure. For 21% ambient oxygen concentration ignition was achieved for carbon dioxide concentrations up to 46% with the remaining being nitrogen. The experimental burning rates were compared to existing theoretical models. A flammability map for n-heptane burning under normal gravity as a function of carbon dioxide concentration and pressure was also developed using these results.     

Model of heterogeneous combustion of small particles

A steady model of heterogeneous combustion for a spherical particle in the transition heat and mass transfer regime is developed. The model assumes formation of condensed products and reaction rate controlled by the transport of oxidizer to the particle surface. The model is based on the Fuchs’ limiting sphere approach. Calculations are performed for combustion of zirconium particles of different sizes. Temperature and oxygen concentration profiles are calculated and compared to those predicted by the continuous medium transfer model. The predictions are compared with available experimental data. For coarse particles, both predicted combustion temperatures and burn rates match respective experimental data when the reaction is assumed to produce zirconium–oxygen solution rather than stoichiometric ZrO₂. A weaker effect of particle size on their burn time is predicted for smaller particles, in qualitative agreement with recent experiments. However, the model underestimates the burn times and overestimates the combustion temperatures for small particles. This discrepancy is likely associated with the finite reaction kinetics at the particle surface that must be accounted for in the future work.     

Group combustion of char/carbon particles

Extensive literature exists for the experimental data on coal/char ignition and combustion. While most of the experiments are performed with a cloud or stream of particles, the theoretical modeling used to compare and interpret the experimental data is based on the individual particle combustion (IPC) model. As opposed to individual particle modeling, a group combustion (GC) theory is proposed for the combustion modeling of char/carbon particles. For a cloud of liquid drops, the group behavior implies the formation of a flame (group flame) around a large number of drops rather than a flame around each drop. More generally, the group behavior for a cloud of particles represents the change in the burning characteristics due to collective behavior of particles with or without a group flame. To gain a basic understanding of the group behavior, a model such as the analysis of a spherically symmetric cloud of particles burning in quiescent air is presented here. Each particle within the cloud produces CO, due to both the oxidation of C to CO and the reduction of CO₂ to CO which subsequently oxidizes to CO₂ in the homogeneous gas phase.

Generalized results for the burning rate and the flame structure are given as a function of group combustion number (G). Predicted results show unexpected results including the independence of the burning rate of CO kinetics. Quantitative results for both the cases of frozen and fast CO kinetics are given. There is a group flame for the case of fast CO kinetics. It is shown that the group flame occurs at G > 5 while for a cloud of liquid drops, the group flame occurs at G > 0.1. The higher critical group combustion number is attributed to the lower burning rate of particle inside the cloud compared to the burning rate of liquid drops inside the cloud. The results show that there exists mainly three modes of combustion: (i) Individual Particle Combustion (IPC, low G), (ii) Group Combustion (GC, intermediate G) and (iii) Sheath Combustion (SC, high G). Criteria are given for identifying the mode of combustion from the experimental conditions. The criteria and the establishment of modes of combustion are independent of the extent of CO kinetics. It is found that the experimental data, obtained with a stream of particles and commonly interpreted with the IPC model, indicate the combustion modes to vary from IPC to SC modes. These data are now reinterpreted with the group theory.     

Ignition and combustion of a gaseous fuel pocket array in an oxidizing environment

ABSTRACT

Ignition and combustion of an infinite linear array of gaseous fuel pockets in a stagnant oxidizing environment under the microgravity condition is studied by a numerical approach. The combustion process is considered isobaric and the fluid motion is induced by density gradients due to the heat and mass transfer processes. A simple finite chemical reaction mechanism and the ideal gas equation of state are considered. The thermophysical properties, except density, are assumed constant. The Finite Volume Method is used with a hybrid non-staggered grid in a generalized system of coordinates. The SIMPLEC algorithm solves the modified pressure–velocity coupling. The Damköhler number effects on flame dynamics and on the fuel consumption are analyzed. Three stages in the burning processes: the induction time, the flame propagation and the diffusive burning are identified. The merging processes of the fuel pockets and of the flames are depicted.     

Observations on the combustion of boron slurry droplets in air

Single fiber-supported slurry droplets composed of boron in JP-10 were ignited and burned in room-temperature air. Initial droplet diameters ranged from 1.2 to 3.0 mm and initial boron weight fractions f from 0 to 0.7. It was observed that although the liquid fuel apparently burns completely the boron does not ignite under these experimental conditions. For the pure liquid the combustion is smooth with a measured burning-rate constant of 0.43 mm²/s. At low f there is periodic swelling of the droplet with mildly disruptive emission of gas from the interior; the severity of this irregularity is greatest for f ≈ 0.1 and negligible for f ≳ 0.2. For f ≲ 0.4 a reduction in droplet diameter, according to a d² law, is observed for a period of time, followed by a burning period of essentially constant diameter. For f ≳ 0.5, the droplet diameter remains practically constant during combustion, although the measured burning time conforms to a d² law. These observations are compared quantitatively with theoretical predictions and are found to agree within accuracies ranging from 10% to 25%.     

Combustion characteristics of GAP-coated boron particles and the fuel-rich solid propellant

A process was employed that permits the coating of energetic glycidyl azide polymer (GAP) on the boron surface. Ignition and combustion behavior of single particle pure crystalline boron and GAP-coated boron at atmospheric pressure was studied experimentally by injecting the particles into the stream of hot gaseous environment of a flat-flame burner using premixed propane-oxygen-nitrogen gases. Chopped streak photographic observation was used to measure the ignition and combustion time. The flame temperature was fixed around 2343 K, but under wider O₂ level range than previous investigations. Measurement results show that GAP coating can shorten boron particle ignition delay time, however, the effect diminishes as the O₂ level in combustion gas decreases. Possible mechanisms based on relevant reactions and heat effects were proposed. Combustion characteristics of fuel-rich solid propellants based on GAP-coated amorphous boron particles and uncoated ones were compared using different techniques such as combustion phenomena observations by a windowed strand burner, quenched propellant surface morphology analysis by scanning electron microscope, and combustion residues size analysis from the quenched particle collection bomb experiments. It was concluded that GAP-coated amorphous-boron-based fuel-rich propellants exhibit more vigorous combustion phenomena, higher burning rates, and a lesser extent of residue agglomeration than the uncoated baseline propellant. Moreover, reaction mechanisms were proposed to elucidate the combustion products obtained in this study.     

Effect of gravity on laminar premixed gas combustion II: Ignition and extinction phenomena

Minimum ignition energies and flame radii as a function of time were measured for near-limit, limit, and sublimit fuel-lean methaneair mixtures burning at one-g and zero-g. Minimum ignition energy values were the same at one-g and zero-g except for mixtures very near the zero-g flammability limit and leaner, where the zero-g values were much higher than the one-g values. For sublimit mixtures at zero-g a previously unreported mode of unstable flame propagation was observed; this mode was characterized by a flame radius increasing in proportion to the square root of the time lapse from ignition, an energy release often orders of magnitude greater than the spark energy input, and sudden extinction. This mode of flame propagation was observed at all gas pressures tested but was more pronounced at higher pressures. All zero-g propagation was spherically symmetric except for a few unusual flame extinguishments at high pressures. The principal conclusions are that flame extinguishment at zero-g is caused by a flame-front instability and that gravitational forces have a stabilizing effect on upward flame propagation. The cause of the instability could not be determined; further experiments which might aid in determining the cause are suggested.     

Modeling and countermeasures of combustion characteristics of char particles in CFBC

INTRAODUCTIONAsahigh-efficiencyandcleancoalcombustiontechnology,circulatingfluidizedbed(CFB)combustiontechnologyachievesrapiddevelopmentinChinaforburningvariouslow--gradefuels.ThescalerupofCFBboilersbecomesakeypointconcernedbytheCFBboilerdesigners.At...     

On possibility of vapor-phase combustion for fine aluminum particles

A simplified heat transfer model applicable for vapor-phase combustion of individual fine metal particles predicts existence of a critical particle diameter, below which the vapor-phase flame alone cannot be self-sustaining. Other heat generation mechanisms (i.e. surface oxidation) should complement the vapor-phase flame. The predicted critical particle diameter is a function of the flame temperature and pressure. For single aluminum particles burning in atmospheric pressure air, CO₂ and H₂O, the predicted critical particle diameters are close to 6, 7, and 15 μm, respectively.     

Gas-phase modeling of homogeneous boron/oxygen/hydrogen/carbon combustion

Boron has practical applications as an advanced fuel in propulsion systems due to its high energy content. The combustion of boron in the presence of hydrocarbon fuels is a complex problem involving heterogeneous particle oxidation followed by gas-phase kinetics of the volatilized boron species. In this study, we have modeled the high-temperature gas-phase combustion chemistry of the B/O/H/C system. We have examined the effects of recent experimental gas-phase kinetic measurements of several of the critical reaction rates and theoretical thermodynamic and transition state calculations on the previous model of boron combustion. Additional reactions that critically affect the combustion efficiency are identified for future experimental and theoretical study. The role of boron oxyhydrides, which are metastable species, is discussed.     

The influence of alkaline catalysts on combustion of coal particles

With increasingly stringent environmental limitations, it is essential to develop and study low-emission combustion techniques such as fluidized bed combustion. In this work, an experimental work was carried out to study the influence of minerals on combustion characteristics of Tabas coal in a one-stage fluidized bed. The results showed that the alkaline minerals have a significant influence on the combustion behavior of coal particles, especially at higher temperatures. It was also found that the residence time has a significant role in both the higher thermal energy and char conversion, due to a considerable increase in the rate of reactions especially at the beginning of the process.