Deflagration Rate Research Articles

Measuring dust burning velocity for deflagration vent design

Deflagration vent design should be based on the burning velocity in the pressure range below 3 bara, where vent relief devices normally operate, rather than the KSt deflagration index, which is typically measured at pressures >50% of the maximum deflagration pressure, Pmax. Tests using a standardized 1000-L vessel showed that in the pressure range below about 3 bara, niacin and lycopodium burned faster than cornstarch, despite its larger KSt index. We attribute this behavior to the endothermic dehydration of cornstarch during the early stages of deflagration. Deflagration vents for cornstarch and other milled grains may have been oversized while vents for some other dusts may have been undersized. Burning velocities are most relevant in the region of the 2-bara midpoint overpressure and can theoretically be found from the “isothermal pressure rate gradient”, or IPRG, which we define as the gradient of (dP/dt) plotted against P (1-1/P)2/3. However, owing to irregular combustion caused primarily by two 5 kJ igniters, the IPRG is found indirectly from the “pressure rate gradient” or PRG, which we define as the gradient of (dP/dt) plotted against P. The PRG was found to be adequately linear for measurement at 2 bara and the experimental curves passed through the "origin". It was shown mathematically that at 2 bara the PRG is 1.05 times larger than IPRG, permitting the IPRG and turbulent burning velocity to be calculated. Since the calculation of burning velocity from the IPRG requires Pmax, a general extrapolation technique was developed for correcting Pmax values obtained in vessels smaller than 1000-L. We propose that, owing to the greater turbulence in the 20-L vessel, a calibration be made using methane. This would establish the turbulence factors for each vessel at 2 bara, allowing the underlying “reference” burning velocities to be calculated and compared. However, to measure turbulent dust burning velocities in 20-L vessels a smaller and more efficient igniter must be used. Two 5 kJ igniters not only obscure the pressure history but wastefully expend energy far from the vessel core, depleting the unburned mixture and depressing the subsequent pressure rate. An observed “double sigmoid” dependence of dust deflagration rate on particle diameter suggests that routine explosibility testing of organic dusts is usually carried out in a region where pressure rates are relatively insensitive to particle size.

Experimental study of the correlation for turbulent burning velocity at subatmospheric pressure

Turbulent burning velocity is one of the most relevant parameters to characterize the premixed turbulent flames. Different correlation has been proposed to estimate this parameter. However, most of them have been obtained using experimental data at atmospheric pressure or higher. The present study is focused on obtaining a correlation for the turbulent burning velocity using data at sub-atmospheric pressure. The turbulent burning velocity was experimentally calculated using the burner method, where turbulent premix flames are generated in a Bunsen burner. Stoichiometric and lean conditions were evaluated at a pressure of 0.85 atm and 0.98 atm, whereas the turbulence intensity was varied for each condition. Perforated plates and a hot-wire anemometer were used to generate and measure the turbulence intensity. Schlieren images were used to obtain the average angle of the flame and calculate the turbulent burning velocity. Experiments and theory show that the turbulent deflagration rate decrease as pressure decrease. The turbulent deflagration speed decreased by up to 16 % at 0.85 atm concerning atmospheric conditions for the same turbulence intensity, discharge velocity, and ambient temperature, according to the experimental results. The comparison among the experimental results at sub-atmospheric conditions and the correlations reported in the literature exposes prediction issues because most of them are fitted using data at atmospheric conditions. A general correlation is raised between turbulent burning velocity (ST), laminar burning velocity (SL) and turbulence intensity (u’) proposed from the experimental data. This correlation has the form For sub-atmospheric and atmospheric conditions, the coefficients were determined

Developing Reaction Chemistry Models from Reactive Molecular Dynamics: TATB

AbstractReactive Molecular Dynamic (RMD) are used to simulate the cook‐off chemistry of TATB at a variety of fixed density and fixed temperature conditions. The chemical transformations are monitored using a Coordination Geometry Analysis (CGA) approach which tracks which atom types are bonded to each specific atom. This particularly identifies oxidation state changes that occur during the transformations. Correlations between these different chemical changes are identified using a Non‐negative Matrix Factorization (NMF) approach. These identify reduced order chemistry models for the TATB system which contains six components whose concentration profiles are a function of both the temperature and density/pressure. The time histories of these transformations appear to show exponential growth/decay properties that could be fit with Arrhenius rates. These components should form the basis of deflagration rate models for these materials which could then be used in mesoscale simulations to analyze accidental initiation, shock‐to‐detonation and detonation propagation.

Experimental investigation of the deflagration rate for PBX utilizing terahertz-wave-based Doppler velocimetry

Determining the deflagration rate of high explosives is important for understanding the evolution of accident reaction and improving the design of charge safety. A noninvasive terahertz-wave-based Doppler velocimetry (TDV) method is demonstrated for measuring the deflagration rate of a polymer-bonded explosive (PBX) under high pressures in a closed burner. The penetration ability of TDV avoids cutting the PBX sample into pieces to embed gauges, thus ensuring the burning surface undisturbed. The development of deflagration rate for the octahydro-1,3,5,7-tetranitro-1,3,5,7-tetranzocine-based PBX-3 agrees with Vielle’s law before pressure increases too high. But at high pressure, unstable burning is observed, implying the transition to convective burning.

Isolating the effects of oxidizer characteristics and catalytic additives on the high-pressure exponent break of AP/HTPB-Composite propellants

AP/HTPB-composite propellants are widely used in the field of energetics due to their burning rate controllability using a variety of formulation variables. At higher pressures, the burning rate becomes less controllable as it experiences a transition regime often referred to as an “exponent break” typically between 20.7 and 34.5 MPa. The pressure exponent drastically increases to values greater than 1, making the burning rate extremely sensitive to pressure fluctuations. This study systematically evaluated the effects of catalysts on the exponent break and high-pressure burning rates of AP/HTPB-composite propellants containing a variety of AP particle sizes, distributions, and concentrations. The burning rates of seven formulations with varying AP characteristics and either Mach I iron oxide or titania nanoparticles or in-situ titania as a catalyst were evaluated between pressures of 6.89 MPa and 68.9 MPa. All formulations with the exception of two, 46.0-µm AP with Mach I titania and 138.9-µm AP with 0.50% in-situ titania, showed an exponent break. For the others, the characteristic pressure where the exponent break occurred changed with the inclusion of the catalysts, increasing it to 34.5 MPa and higher. The characteristic pressure was found to be dependent on the corresponding baseline burning rates, occurring where the additive burning rate curve intersected with its respective baseline burning rate curve. Additionally, all the burning rates fell above the AP deflagration rate curve, corroborating the existence of an AP barrier and the general theory in the literature that AP decomposition dominates in the very-high-pressure regime. This study adds new data to the severely limited database for very-high-pressure, AP-based, composite propellant burning rates in the open literature and provides one of the first fundamental studies on the exponent break feature with emphasis on the role of mixture variables and catalytic additives on the characteristic break pressure and the post-break pressure exponent.

Characterization of display pyrotechnic propellants: Burning rate

The combustion of display pyrotechnic propellants utilized for producing colored light has been studied. The linear burning rates of cylindrical propellant strands were measured using high-speed videography. The experiments were conducted with air at atmospheric pressure as the surrounding medium mimicking the conditions of unconfined aerial combustion typically encountered for these propellants. Five different formulations of display pyrotechnic propellants producing red, green, blue, yellow, and silver color were tested. The flame zone was observed to be situated very close to the propellant surface and the colored flame extended beyond this point. The phenomenology of the combustion process was explained and the combustion process was also studied numerically using a methodology based on the deflagration rate law. The experimentally measured burning rates were utilized in the deflagration rate law to obtain the simulation parameters which may be utilized in hydrocodes for performance prediction and simulation pyrotechnic propellant applications.

Deflagration of HMX‐Based Explosives at High Temperatures and Pressures

AbstractWe measure the deflagration behavior of energetic materials at extreme conditions (up to 520 K and 1 GPa) in the LLNL High Pressure Strand Burner, thereby obtaining reaction rate data for prediction of violence of thermal explosions. The apparatus provides both temporal pressure history and flame time‐of‐arrival information during deflagration, allowing direct calculation of deflagration rate as a function of pressure. Samples may be heated before testing. Here we report the deflagration behavior of several HMX‐based explosives at pressures of 10–600 MPa and temperatures of 300–460 K. We find that formulation details are very important to overall deflagration behavior. Formulations with high binder content (≥15 wt%) deflagrate smoothly over the entire pressure range regardless of particle size, with a larger particle size distribution leading to a slower reaction. The deflagration follows a power law function with the pressure exponent being unity. Formulations with lower binder content (≤10 wt% or less) show physical deconsolidation at pressures over 100–200 MPA, with transition to a rapid erratic deflagration 10–100 times faster. High temperatures have a relatively minor effect on the deflagration rate until the HMX β→δ phase transition occurs, after which the deflagration rate increases by more than a factor of 10.

Reaction Propagation Rates in HMX at High Pressure

AbstractWe have measured the reaction propagation rate (RPR), or deflagration rate, in octahydro‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocine (HMX) powder in a diamond anvil cell over the pressure range 0.7–35 GPa. Numerical simulations of the RPR of pressurized HMX were also performed for comparison to the experimental results obtained. The simulated RPR values closely approximate the observed rates at pressures up to 3 GPa, and serve as a bridge to lower‐pressure deflagration rates for HMX in the literature. However, at higher pressures the simulated RPR values deviate significantly from our experimental results. This suggests that further refinement to the computational model is required for the calculated RPR values to approach those observed at higher pressures.

Ignition & Growth and JWL++ Detonation Models in Coarse Zones

“Ignition & Growth” (I&G) and JWL++ models are compared for a variety of problems. The detonation velocity becomes nearly constant with zoning at the edge of convergence, which for TATB, is 8 zones/mm for I&G and 4 for JWL++. The use of pressure in the rate for I&G makes the detonation velocity rapidly decrease as the zones are coarsened. Using pressure plus artificial viscosity to some power in the rate for JWL++ allows the correction for coarsening zones. In coarse zones, the pressure and the burn fraction turn on independently and this feature dominates model behavior. If pressure lags burn fraction, then the maximum pressure will be lower than expected. An unexpected phenomenon is saturation, i.e. the slowing down of the detonation velocity as a function of the fast rate constant. This slowing can be weak and produce a plateau, or it can be strong and cause the detonation velocity to approach an asymptote. The saturation effect comes from a combination of the 1−F term and declining pressures. Failure (critical diameter effect) occurs in reactive flow but optimizing for this undoes the settings for other results. In JWL++ , the fast reaction pressure exponent is near −1 for the best fit for the size (diameter) effect, 2 for the Pop plot and near −3 to fit failure. The Pop plot deflagration rate is derived, although it needs not to be the same as the detonation rate. The use of additive pressures is compared with the pressure equilibrator and no difference is found. Increased zoning by a factor of 5 and improved code structure will be needed for future improvement.

Dependence of AP Deflagration Rate on Details of Test Sample Preparation

Dependence of AP Deflagration Rate on Details of Test Sample Preparation

Steady Deflagration of HMX With Simple Kinetics: A Gas Phase Chain Reaction Model

A new approach is presented for modeling steady combustion of energetic solids, in particular HMX. A simplified, global, gas phase chain reaction kinetic mechanism is employed. Specifically, a zero-order, high activation energy thermal decomposition initiation reaction in the condensed phase followed by a second-order, low activation energy chain reaction in the gas phase is assumed. A closed-form solution is obtained, which is based on the activation energy asymptotics analysis of Lengelle in the condensed phase and the assumption of zero activation energy in the gas phase. Comparisons between the model and a variety of experimental observations over a wide range of pressures and initial temperatures are presented and demonstrate the validity of the approach. The model provides excellent agreement with burning rate data (including sensitivity to pressure and initial temperature) and temperature profile data (in particular the gas phase). This suggests that in the realm of simplified, approximate kinetics modeling of energetic solids, the low gas phase activation energy limit is a more appropriate model than the classical high activation energy limit or heuristic flame sheet models. The model also indicates that the condensed phase reaction zone plays an important role in determining the deflagration rate of HMX, underscoring the need for better understanding of the chemistry in this zone.

Particle radiative feedback in ammonium perchlorate deflagration

The deflagration behavior of ammonium perchlorate (AP) with carbon black and copper chromite catalyst additives was studied over a pressure range of 4.3-171 MPa (50-2500 psig) using light transmission and emission measurements in a window bomb and burn rate measurements in a conventional strand burner. It was found that a maximum value of the lower pressure limit PDL exists at intermediate values of carbon black concentration similar to that already reported for copper chromite catalyst. It was also found that sufficiently high concentrations of carbon black augment the steady deflagration rate of AP. Since carbon black is not a catalyst of AP decomposition , it is postulated that particle radiative feedback is more likely to be the cause of the observed behavior than previously suggested catalyst effects. To quantify the amount of radiative heat feedback, flame temperature and emissivity values were calculated from light emission/transmission measurements. These calculations yielded flame temperatures between 1406 and 1449 K and a value for the effective particle absorption efficiency over diameter Qa/d of 4.1 jun1 in good agreement with expected values. A simple analysis shows that the observed trends (increasing PDL at low particle concentrations and decreasing PDL at higher concentrations) can be predicted from simple radiative transfer considerations together with particle and matrix continuity equations.

The deflagration of single crystals of ammonium perchlorate

By means of high-speed motion photography the deflagration rate of single crystals of pure ammonium perchlorate was measured from the deflagration pressure limit to 5000 psia at ambient temperatures of 89, 23, and −28°C. The 23°C burning rate isotherm, which was consistently lower than the 89°C isotherm and above the −28°C isotherm, rose to a relative maximum, dropped to a relative minimum, and then rose again as the pressure was increased to 5000 psia. The −28°C isotherm was measured between 415 and 565 psia and between 2000 and 4500 psia and had an apparent discontinuity between these two pressure regions. Within the accuracy of the data the deflagration rate was not influenced by the pressurization gas, either nitrogen or helium, by the crystallographic axis of the deflagration wave proceeding through the crystal, or by natural convection.

Deflagration rate, surface structure, and subsurface profile of self-deflagrating single crystals of ammonium perchlorate

Pure ammonium perchlorate single crystal self deflagration, determining energy transfer mechanisms from pressure effects, combustion characteristics and subsurface profile

Investigation of the AP composite solid- propellant deflagration mechanism by means of experimental analog techniques.

The composite solid-propellant deflagration mechanism has been studied experimentally by means of two laboratory burner techniques. The techniques allow experimental parameter variations that are impossible with the propellants (due to their structural pecularities) . The burner is composed of oxidant and fuel granules and has deflagration characteristics that are almost perfectly analogous to those of actual ammonium perchlorate (AP) propellants. The burner involves a bonded, porous AP bed that burns at the surface with emerging fuel gas passed up through the bed; similarly, porous fuel beds are burned with oxidant gas. The close analogy of the loose-granule burner is destroyed (by interstitial flame penetration) at combustion pressures greater than about 50 psia. The porous-plug burner surface emits burning AP crystals at methane throughputs greater than approximately that calculated to yield stoichiometrically correct combustion, thus limiting the analogy as well as suggesting reexamination of the work of others who used such burners to infer the stoichiometry of AP systems. Results from the analog techniques indicate that the propellant deflagration rate is sensitive to fuel-pocket size (which sets the scale of granularity) and details of the fuel combustion process (in addition to over-all energy release).

The deflagration of hydrazine diperchlorate

Experimental studies encompassing the following aspects of the self-deflagration of the solid oxidizer hydrazine diperchlorate have been carried out: deflagration rate as a function of pressure and the effects of catalysts; flame demperature and temperature profile through the combustion wave; thermal decomposition and quenching of the deflagration. The results suggest that the deflagration process is defined by three pressure regimes; a low-pressure régime, below approximately 20 atm; a high-pressure régime, above approximately 100 atm; and a region of transition. A high pressures, ‘normal’ deflagration occurs, i.e. a flame is stablized above the oxidizer heat from the exothermic reaction zone is transmitted back to the condensed material causing gasification. Reactants enter the flame and thus continue the cycle. At pressures below 20 atm, the oxidizer is mainly consumed by a rapid, self-sustaining decomposition. Condensed phase chemical reactions are the primary mode of combustion and heat transfer from a stable flame makes a secondary contribution to the process.

Deflagration characteristics of ammonium perchlorate at high pressures

Influence of very high pressure /1000 - 23000-psi/ on deflagration rate of pure ammonium perchlorate