Burning Rate Enhancement Research Articles

Burning rates and temperatures of flames in excess-enthalpy burners: A numerical study of flame propagation in small heat-recirculating tubes

This study investigates flame propagation in small thermally-participating tubes where the wall acts as a heat-recirculating medium. This fundamental configuration allows heat in the combustion products to be recirculated into the reactants, resulting in excess enthalpy and enhanced burning rates. Preheating of the reactants by heat recirculation has traditionally been considered to be the dominant mechanism leading to large burning rates observed in such systems. This is mainly supported by results from physical models based on a one-dimensional (1-D) representation of the system, where the radial diffusion of heat from wall surface to channel centerline is not accurately captured. In this study, a 2-D formulation with conjugate heat transfer, which accurately resolves the transport of heat inside the gas-wall system, is used to model the excess-enthalpy phenomenon. Steadily-propagating stoichiometric methane–air flames are simulated inside an adiabatic tube of finite wall-thickness, over a wide range of inlet flow velocities and small tube diameters. Burning-rate enhancement is found to be caused not only by preheating, associated with heat recirculation, but also by an increase in flame-front area. Flame elongation is more pronounced with increasing tube diameter and inlet velocity, up to a point where the change in flame-front area becomes dominant in enhancing burning rate. In that case, heat recirculation is a necessary condition for flames to couple to the thermal wave in the wall and elongate, but does not provide a significant increase in enthalpy or temperature that would otherwise be needed for high burning rates to be observed. As the diameter is reduced, the effect of preheating becomes increasingly important for burning-rate enhancement compared to flame area increase. At very small diameters, smaller than the flame thickness, the increase in burning rate is seen to be predominantly attributable to preheating. However, preheating is seen to become limited as inflow velocity is increased, due to 2-D effects inside the fluid that interfere with heat recirculation. These findings demonstrate that 2-D effects inside the fluid can have a prohibitive influence on the burning-rate enhancement attributed to preheating, but that they also give rise to an additional mechanism, associated with the change in flame surface area, responsible for burning-rate enhancement in heat-recirculating burners.

Bi-metallic nanocomposites of Mn with very high catalytic activity for burning rate enhancement of composite solid propellants

Bimetallic nanocomposites of Mn with Co, Ni and Zn were successfully synthesized by polyol method. Particles of the nanocomposites varied in shape from spherical to cubic having an average size of the order of 9–18nm. The nanocomposites showed very high activity as burning rate catalysts for composite solid propellants (CSPs) containing hydroxyl terminates polybutadiene (HTPB) as binder and ammonium perchlorate (AP) as oxidizer. MnCo was the best catalyst among the three nanocomposites as it enhanced the burning rate of the CSP to more than three fold. Catalytic activity of the nanocomposites for thermal decomposition of AP and CSPs was investigated by simultaneous thermogravimetric analysis–differential scanning calorimetry (TGA–DSC) and ignition delay measurements. MnCo was found to be the best catalyst in terms of lowering decomposition temperature of both AP and CSPs. Kinetics of catalyzed thermal decomposition of AP was also studied using isoconversional method from isothermal TGA data.

Turbulent premixed flames on fractal-grid-generated turbulence

A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area.

Electrospun Nanofiber-Based Thermite Textiles and their Reactive Properties

In this work, we present a first time fabrication of thermite-based nanofiber mats with a nitrocellulose composite energetic binder to create a new class of energetic 1D nanocomposite. The as prepared thermite based nanofibrous mats were characterized and tested for their burning behavior, and compared with the pure nitrocellulose and nanoaluminum incorporated nanofibers for their combustion performances. Thermite-based nanofibers show enhanced burning rates in combustion tests, which correlate to the mass loading of nanothermite relative to binder in nanofibers. The electrospinning method demonstrates the possibility of avoiding some of the problems associated with melt casting nanometalized propellants.

Experimental Investigation of High-Burning-Rate Composite Solid Propellants

B ECAUSE motor thrust depends on the product of the exposed burning surface area and the propellant burning rate, high burning rates provide the ability to generate high thrust levelswithout the need for elaborate grain designs that provide high-burning surface areas. Complex, high-surface-area grain designs suffer from the fact that they reduce volumetric loading fraction (the ratio of propellant volume to chamber volume), which is one of the leading reasons for missiles’ size and weight. In addition, complex grain designs are more subject to mechanical failure under the harsh operational conditions of high-thrust/high-acceleration missiles. For these reasons, high-burning-rate propellants provide an enabling technology for a number of important missions. Ideally, alternatives can be identified that lie within the hazards class 1.3 propellant classification such that handling is less involved and the devices are inherently safer to personnel working with the system. It is well known that burning rates increase as particle sizes are decreased because the flame zone lies closer to the propellant surface where it provides more subsurface heating which drives the overall process. Because ammonium perchlorate (AP) is the most common oxidizer used in today’s composite solid propellants, there are numerous studies [1–5] that have shown burning rates increase inversely with AP particle size. The well-known Beckstead et al. multiple-flamemodel predicted a substantial increase in burning rate as AP particle size was decreased [6]. For unimodal distributions, their results showed an asymptotic ‘premixed flame’ limit that was approached at AP particle sizes somewhat below 10 m. From a practical standpoint, propellant processing limits preclude the use of this variable to a significant extent. In addition, very fine AP powder is more hazardous; particle sizes less than 15 m are classified as explosive by the U.S. Department of Transportation. Despite these drawbacks, one of the most effective strategies to increase burning rate is to minimize AP particle size such that mix viscosity and the desired hazards classification are met. Aluminum powder is the most common fuel in composite solid propellants, and reduction of its particle size has similar effects in increasing burning rate as with AP. The effect of aluminum content and powder size on burning rate has been studied in the classical literature [7–9] and has been the subject of more recent literature [10,11] with the development of nano-aluminum (nAl). Nanoaluminum has been proven to considerably enhance propellant burning rates over coarse aluminum. Shalom et al. showed in [12] that replacement of half of a propellant formulation’s 18% (by weight) coarse aluminum with nano-aluminum or ultrafine aluminum (UFAl) increased the burning rate by 84%. Using a unimodal aluminum distribution to determine the effect of particle size, Galfetti et al. [13] showed that replacing all of the micron-size aluminum in an AP/Al/hydroxyl-terminated polybutadiene (HTPB) (68/15/17) propellant increased the burning rate by 100%. Dokhan et al. in [11] showed that the addition of UFAl increased burning rate and that a higher fine-to-coarse AP ratio, in addition to the UFAl, further enhanced burning rate. With only 20% of the aluminum loading being UFAl, Dokhan et al. [11] showed that a burning-rate increase of 160% was delivered by increasing the fine AP loading from 20 to 40% and that a further 38% increase in burning rate could be realized with a fine AP loading of 60%. In addition to the effect of the fine AP loading, Dokhan et al. [11,14] obtained results that showed, for bimodal cases, substantial burning-rate increases occur at UFAl loadings as small as 20% of the total aluminum loading. Burn-rate catalysts or ‘modifiers’ are another commonmethod for enhancing burning rates of composite solid propellants. Extensive research regarding burn-rate modifiers has been conducted since the second half of the 1960s [1,3,15–25]. It has been shown that Received 18 January 2012; revision received 23 April 2012; accepted for publication 28 April 2012. Copyright © 2012 by Timothy D. Manship, Stephen D. Heister, and Patrick T. O’Neil. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0748-4658/12 and $10.00 in correspondence with the CCC. ∗Graduate Student, School of Aeronautics and Astronautics, 500 Allison Road. Member AIAA. Professor, School of Aeronautics and Astronautics, 500 Allison Road. Associate Fellow AIAA. Graduate Student, School of Mechanical Engineering, 500 Allison Road. Member AIAA (Corresponding Author). JOURNAL OF PROPULSION AND POWER Vol. 28, No. 6, November–December 2012

EFFECT OF BALLISTIC MODIFIERS ON THE BURN RATE OF EXTRUDED COMPOSITE PROPELLANT FORMULATIONS BASED ON THERMOPLASTIC ELASTOMERIC BINDER

The effect of ballistic modifiers on the burn rate of extruded composite propellant (ECP) formulations primarily based on ammonium perchlorate (AP) as oxidizer, aluminum (Al) as metallic fuel, and thermoplastic polyurethane, viz., Irostic® as binder, has been investigated. The ballistic modifiers, viz., iron oxide (Fe2O3), copper chromite (CuCr2O4), and strontium carbonate (SrCO3), were studied in the concentration varying from 0.2 to 1.0 part above 100 parts of base composition. The results obtained reveal that the burn rate increases with increase in the concentration of Fe2O3 and CuCr2O4. Maximum burn rate enhancement is observed with 1 part of Fe2O3, which is of the order of 130%. The results are discussed in detail in the light of thermal decomposition data generated on polymer and propellant compositions using ballistic modifiers.

Study on Poly(ferrocenylsilane) and Its Promotive Effect to Decomposition of Ammonium Perchlorate

S OLID propellant is one of the most significant ingredients used in rockets. The burning rate of propellant is a vital parameter for rocket design. A promising method to enhance the burning rate of propellants is to use burning-rate promoters (BRPs). BRPs have become increasingly important and are receiving more attention recently due to their successful use in solid propellant burning-rate enhancement. Generally, there are several kinds ofBRPs; transitionmetal oxides, nanometal particles, metal chelate, ferrocene, and its derivatives. Transition metal oxide BRPs are cheap, but the burning-rate improvement of propellant is limited. The addition of nanometal particles can enhance the burning rate because nanometal particles have large specific surface areas and higher surface energy. However, nanometal particles are difficult to disperse well and passivation is needed for their surface to prevent spontaneous combustion in air [1]. Organic metal chelate BRPs, such as copper organic chelate and Plumbum iron double metal chelate, can greatly enhance the burning rate due to their good dispersion in propellants. Ferrocene and its derivatives have attracted much attention for their fascinating properties as BRPs [2]. They have been widely used in composite propellant, especially to enhance the burning rate of butyl hydroxide propellant, which contains ammonium perchlorate (AP) and aluminum powder. When ferrocene and its derivatives are used as BRPs, they are easy to migrate during storage. This migration affects their application in propellants. In this Note, we explore the possibility of using a series of poly(ferrocenylsilanes) with highmolecular weights as BRPs.

Flame speed predictions in planar micro/mesoscale combustors with conjugate heat transfer

An analytical model for flame stabilization in meso-scale channels is developed by solving the two-dimensional partial differential equations associated with heat transport in the gas and structure and species transport in the gas. It improves on previous models by eliminating the need to assume values for the Nusselt numbers in the pre and post-flame regions. The effects of heat loss to the environment, wall thermal conductivity, and wall geometry on the burning velocity and extinction are explored. Extinction limits and fast and slow burning modes are identified but their dependence on structure thermal conductivity and heat losses differ from previous quasi one-dimensional analyses. Heat recirculation from the post-flame to the pre-flame is shown to be the primary mechanism for flame stabilization and burning rate enhancement in micro-channels. Combustor design parameters like the wall thickness ratio, thermal conductivity ratio, and heat loss to the environment each influence the flame speed through their influence on the total heat recirculation. These findings are used to propose a simple methodology for preliminary micro-combustor design.

HIGH-NITROGEN METAL COMPLEXES AS BURNING-RATE MODIFIERS FOR THE ALUMINUM-WATER PROPELLANT SYSTEM

The reactions of electropositive metals, such as aluminum, with water have long been utilized in explosive and propellant formulations, but until recently this has mostly been limited to the water formed as a product gas from the decomposition of another energetic system . Recently, however, with the increased availability of nano-particulate materials, the direct reaction of nano-aluminum (nAl) with water as an oxidizer has been investigated as a propellant system due to high reaction temperatures and the production of hydrogen as the primary gaseous species. This system could be useful for intra-planetary travel where non-terrestrial water is harvested for the oxidizer. Here we present the study of nAl, mixed at a stoichiometric ratio with water ({Phi} = 1) with the highly water soluble metal complexes of bis(tetrazolato)amine (BTA) added at 5, 15,30 and 50 wt% in the case of FeBTA and 5 and 15 wt% in the case of NiBTA and CoBTA. The basic structure of the BTA complexes is shown below where M = Fe, Ni or Co, and x = 3 for Fe and Co and x = 2 for Ni. The particle size of nAl studied was primarily 38 nm with various studies with the particle size more » of 80 nm. The FeBT A at a loading of 15 wt% gave the highest burning rate enhancement (4.6x at {approx}6.8 MPa), while retaining a low pressure exponent (0.21 compared to 0.24 for nA/H{sub 2}O). At 15 wt% the Ni and Co increased the burning rate, but also increased the pressure exponents. The burning rate of the FeBTA modified material with 80 nm Al decreased as the weight percent of FeBTA was increased, which also tracked decrease in the calculated specific impulse of the mixtures. « less

A wind tunnel experimental study on burning rate enhancement behavior of gasoline pool fires by cross air flow

The data set of our previous experiments in a wind tunnel is re-analyzed and interpreted in this paper in order to provide a more focused description of the manner the cross-flow affects the burning rate of gasoline pool fires. It was unexpectedly found that the burning rates (mass consumption rate per unit area) under a certain level of cross air flow decrease with pool size, which is opposite to that in quiescent air condition where the burning rates increase with pool size. The temperatures of the trailing, parallel-stream side rim walls were increased greatly, while those of the leading rim wall and the bottom changed relatively little when imposing a cross air flow. The burning rate of gasoline pool fire increased with cross air flow speed linearly in this range. The enhancement rate, defined as Δ m ˙ / u , was found to be mainly attributed to heat supplied from the trailing and parallel-stream side walls of the pool, due to the significant increase in their temperature difference with the adjacent fuel. A phenomenological model deduced the enhancement rate to vary linearly with (2 L/ W + 1)/ L. The experimental data was in good agreement with the theoretical analysis.

Exploring the Effects of Nanostructured Particles on Liquid Nitromethane Combustion

Monopropellants consisting of liquid nitromethane and high-surface-area particles of silicon- and aluminum-based oxides were examined to determine the effects of low concentrations of nanostructured materials on deflagration processes. The combustion rates were characterized by measuring linear burning rates in a large pressure vessel filled with argon. Results showed that nitromethane burning rates may be increased at lower pressures with dilute additions of particles. Increases in nitromethane burning rates of greater than 50 % were found with less than 1.0 wt% of particle addition at a nominal pressure of 5.24 MPa. The particle additions were estimated to have only small effects on the equilibrium flame temperatures, density, viscosity, and specific heat. Nitromethane with particle additives displayed a lower burning-rate equation pressure exponent (i.e., reduced pressure sensitivity), which was inversely proportional to particle concentration. Above a pressure of approximately 9 MPa, up to the maximum test pressure (∼14 MPa), the particle additives did not affect the nitromethane burning rate. Condensed-phase temperature profiles of the deflagrating fluid, surface tension, and fluid thermal conductivities were measured in order to elucidate some of the mechanisms causing enhanced burning rates at lower pressures.

Activated charcoal – A novel burn rate enhancer of aluminized composite propellants

This paper reports the discovery of activated charcoal as an effective burn rate enhancer of aluminized composite solid propellant. Experiments were carried out using a strand burner at pressures ranging from 10 to 70 bar with varying fractions of activated charcoal. The results show that with the addition of activated charcoal in an aluminized composite propellant higher burn rates (in excess of 25 mm/s at 70 bar) were obtained. This paper also explores the possibility of further enhancing the burn rates of aluminized composite propellant by using iron oxide along with activated charcoal. Burn rates recorded with iron oxide and activated charcoal both present in the propellant were in excess of 50 mm/s at 70 bar. It was noticed that these high burn rates were accompanied by a higher (0.65) pressure index of combustion. A series of experiments were designed to understand the burn rate enhancement with activated charcoal in aluminized composite propellant. TGA and DSC tests were carried out on AP pellets with and without activated charcoal to detect any condensed phase activity of activated charcoal. These tests did not show any significant difference between the AP pellets with and without activated charcoal. The AP pellets with and without activated charcoal were also burnt in a strand burner to understand if any gas phase reaction was being catalyzed by activated charcoal. AC does not enhance any gas phase activity while addition of AC in AP increased the LPDL of AP and reduced the burn rate. Lastly, sandwich propellant with activated charcoal at the interface was prepared to determine if interface reactions were being affected with the addition of activated charcoal. It has been observed that with the addition of activated charcoal at the AP–binder interface the burn rates are higher than those recorded without activated charcoal at the AP–binder interface.

Droplet combustion in presence of airstream oscillation: Mechanisms of enhancement and hysteresis of burning rate in microgravity at elevated pressure

The enhancement and hysteresis behavior of the burning rate of single droplet combustion in the presence of airstream oscillation observed in previously performed microgravity experiments at elevated pressure up to 1.0 MPa were numerically investigated. Excellent agreement with the experimental results was obtained and the mechanisms of these phenomena were examined based on precise numerical data on instantaneous droplet diameter variations corresponding to the unsteady airstream velocity, flow fields around the droplet, and flame movement during combustion. Results show that, depending on the oscillation Reynolds number, which is a function of pressure, flow amplitude and droplet diameter, there are three mechanisms involved in the enhancement of burning rate. In the cases of low oscillation Reynolds numbers, a diffusion-time-delay has a significant effect on the flame front movement and thus, on heat from the flame to the droplet. In the cases of high oscillation Reynolds numbers, a vortex generated outside the droplet flame promotes the motion of the flame, especially in the wake region, and thus enhancing the droplet burning rate. In addition to these two mechanisms, the forced convection during the acceleration period of the flow oscillation causes overshooting of the droplet burning rate due to instantaneous imbalances of the airflow momentum with the Stefan flow. These three mechanisms explain the predominant role of the highest velocity of the oscillatory airstream in determination of the mean burning rate constant and droplet lifetime. Results also show that the hysteresis behavior of the burning rate is a consequence of the different responses of the flame to the deceleration period compared with the responses to the acceleration period under the existence of those three mechanisms.

Thermal-drag and Transition from Quasi-steady to Highly-unsteady Combustion of a Fuel Droplet in the Presence of Upstream Velocity Oscillations

Numerical studies on the behaviors of combustion of 1-butanol fuel droplet at presence of upstream velocity oscillation are performed. Fuel droplet has an initial diameter of 1.25 mm and ambiance pressure and temperature are 0.4 MPa and 300 K, respectively. These conditions are those in which the microgravity experiments in literature conducted. In the excellent agreement with the experimental data, numerical results show a significant enhancement of the burning rate of droplet compared to what is predicted by quasi-steady film theory models. The mechanism of the enhancement of burning rate is clarified then by observation of a new mechanism that is named thermal-drag, TD. It is shown, depending on the amplitude and frequency of the upstream velocity oscillation, the flame in wake region of droplet can move toward the droplet surface by the force of vortex flow motions produced by the TD mechanism. It is verified that such movement of the flame is responsible for the enhancement of the burning rate and deviation of the response of the evaporation process form the predictions of the quasi-steady model. Frequency analysis of the burning rate reveals that at low frequency and amplitude the FFT diagram of the burning rate contains of only one main peak synchronies with the frequency of upstream velocity oscillation, which implies a quasi-steady response. However; at high frequency and amplitude the diagram includes of wide range of frequencies beside of the main peak that readily shows deviation from the quasi-steady conditions. In the latter, the study on the response of the combustion to the upstream velocity fluctuations in which the fluctuations contains of three wave numbers shows the amplification of the effects of low frequency fluctuations rather than that of damping of the effects of high frequency fluctuations on the evaporation processes.

Mechanism of Solid Propellant Combustion Submitted to a High Plasma Flux

AbstractA simplified mechanism of the plasma effect on the combustion on different types of propellants is presented. The model provides a semi‐quantitative prediction of the burning rate enhancement that should be expected for a given propellant composition and structure. Depending on the propellant structure and composition, one expects a burning rate enhancement either to disappear or to survive a certain time after the plasma injection has been turned off. In order to estimate the internal front propagation rate, we have built a simplified model of the RDX ignition inside the matrix. A cubic lattice topology has been assumed and the ignition front extends from one layer to its nearest neighbor. The propagation rate was found to be dependent on the lattice constant, the particle size, the thermo‐chemical properties of the RDX particles and the matrix background.

Theoretical Analysis of Plasma Enhancement of Propellant Burning Rate

AbstractA theoretical model of the combustion of a nitramine solid propellant in the presence of a plasma jet is proposed. Unlike standard double‐base compositions, nitramine propellants exhibit experimental evidence that plasma induces a burning rate enhancement. The model is based on heat transfer considerations and proposes a closed‐form solution of the enhancement of the propellant burning rate as a function of the thermophysical parameters of the system. The model provides a good qualitative agreement with experimental results.

Tunnel Fires: Experiments on Critical Velocity and Burning Rate in Pool Fire During Longitudinal Ventilation

In this study, the 1/20 reduced-scale experiments using Froude scaling are conducted to investigate the effect of longitudinal ventilation velocity on the burning rate in tunnel fires. The methanol pool fires, acetone pool fires, and n-heptane pool fires with a heat release rate ranging from 2.02 to ~6.15 kW, 2.76 to ~11.04 kW, and 2.23 to ~15.6 kW, respectively, are used. A load cell is used to measure the mass loss rate of the burning fuel and the temperature distributions are measured by K-type thermocouples in order to investigate smoke movement. The ventilation velocity in the reduced-scale tunnel is controlled by the wind tunnel through an inverter. In the case of a methanol pool fire, the increase in ventilation velocity reduces the burning rate. On the contrary, for acetone and n-heptane pool fires, the increase in ventilation velocity leads to the enhanced burning rate of fuels. The reason is that, for acetone and n-heptane pool fires, the oxygen supply effect prevails rather than the cooling effects as the ventilation velocity increases. However, for a methanol pool fire the cooling effect outweighs the effects of oxygen supply. The relationship between the critical velocity (Vc, m/s) and the heat release rate (Q, MW), for a full tunnel, has been found to be:[ILLEGIBLE].

CFD analysis of gas explosions vented through relief pipes

Vent devices for gas and dust explosions are often ducted to safe locations by means of relief pipes. However, the presence of the duct increases the severity of explosion if compared to simply vented vessels (i.e. compared to cases where no duct is present). Besides, the identification of the key phenomena controlling the violence of explosion has not yet been gained. Multidimensional models coupling, mass, momentum and energy conservation equations can be valuable tools for the analysis of such complex explosion phenomena. In this work, gas explosions vented through ducts have been modelled by a two-dimensional (2D) axi-symmetric computational fluid dynamic (CFD) model based on the unsteady Reynolds Averaged Navier Stokes (RANS) approach in which the laminar, flamelet and distributed combustion models have been implemented. Numerical test have been carried out by varying ignition position, duct diameter and length. Results have evidenced that the severity of ducted explosions is mainly driven by the vigorous secondary explosion occurring in the duct (burn-up) rather than by the duct flow resistance or acoustic enhancement. Moreover, it has been found out that the burn-up affects explosion severity due to the reduction of venting rate rather than to the burning rate enhancement through turbulization.

Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity

A flamelet approach is adopted in a study of the factors affecting the volumetric heat release source term in turbulent combustion. This term is expressed as the product of an instability enhanced burning rate factor, P bi , and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression for P bi are a pdf of the flame stretch rate and a flame stretch factor. Fractal considerations link the turbulent burning velocity normalised by the effective rms turbulent velocity to P bi . Evaluation of this last parameter focuses on problems of (i) the pdfs of the flame stretch rate, (ii) the effects of flame stretch rate on the burning rate, (iii) the effects of any flamelet instability on the burning rate, (iv) flamelet extinctions under positive and negative flame stretch rates, and (v) the effects of the unsteadiness of flame stretch rates. The Markstein number influences both the rate of burning and the possibility of flamelet instabilities developing which, through their ensuing wrinkling, increase the burning rate. The flame stretch factor is extended to embrace potential Darrieus–Landau thermo-diffusive flamelet instabilities. A major limitation is the insufficient understanding of the effects of negative stretch rates that might cause flame extinction. The influences of positive and negative Markstein numbers are considered separately. For the former, a computed theoretical relationship for turbulent burning velocity, normalised by the effective rms velocity, is developed which, although close to that measured experimentally, tends to be somewhat lower at the higher values of the Karlovitz stretch factor. This might be attributed to reduced flame extinction and reduced effective Markstein numbers when the increasingly nonsteady conditions reduce the ability of the flame to respond to changes in flame stretch rates. As the pressure increases, Markstein numbers decrease. For negative Markstein numbers the predicted values of P bi and turbulent burning velocity are significantly increased above the values for positive Markstein numbers. This is confirmed experimentally and these values are close to those predicted theoretically. The increased values are due to the greater stretch rate required for flame extinction, the increased burning rate at positive values of flame stretch rate, and, in some instances, the development of flame instabilities. At lower values of turbulence than those covered by these computations, burning velocities can be enhanced by flame instabilities, as they are with laminar flames, particularly at negative Markstein numbers.

Simplified Modeling of Deflagration in Vessels

A simplified method that models the deflagration process occurring in closed or vented vessels is described. When combustion occurs within the spherical or cylindrical vessels, the flame moves spherically or segmentally to the vessel periphery. The volume and area of each element along the propagating flame front are calculated by using simple geometrical rules. For instabilities and turbulence resulting in enhanced burning rates, a simple analysis results in reasonable agreement with the experimental pressure transients when two burning rates (a laminar burning rate prior to the onset of instability and an enhanced burning rate) were used. Pressure reduction caused by a vent opening at predetermined pressure was modeled. Parameters examined in the modeling include ignition location, mixture concentration, vented area, and vent opening pressure. It was found that venting was effective in reducing the peak pressure experienced in vessels. The model can be expected to estimate reasonable peak pressures and flame front distances by modeling the enhanced burning rates, that is, turbulent enhancement factor.