Thermal loading of explosives--finite difference method with time step reduction.
The method of simulation of heat transfer during thermal loading of energetic materials is introduced. The combination of the simple finite difference method with a time step reduction enables the quick and precise calculation of ignition times. The results are in accordance with published model data. The method was also used to simulate heat transfer during the slow cookoff test and the result agrees very well with experimental data.
Bulk Thermal Stability Characterization via the SBAT Apparatus
The temperature at which a substance ignites is a key parameter for safety and design. That temperature, often called the auto-ignition temperature, is not an intrinsic property but depends on the environment in which the substance is found. Energetic substances are unstable and decompose at increasing rates with increasing temperature. Heat is generated by the decomposition of the substance and that heat can then be lost to the surroundings. An energetic substance can rapidly decompose beginning when the rate of heat generation exceeds the rate of heat loss. The temperature at which the onset of ignition occurs depends on the rate of heat loss which is a strong function of its surroundings. The auto-ignition temperature can be found for conditions where heat loss from the sample is high (e.g. using a Differential Scanning Calorimeter or DSC) or when the heat loss is low (e.g. using an Accelerating Rate Calorimeter or ARC). The auto-ignition temperature can differ by more that 50°C for these two conditions. Both the amount of insulation and the heating rate can affect the auto-ignition temperature with higher heating rates or less insulation yielding a higher observed temperature of auto-ignition. The Simulated Bulk Auto-Ignition Test (SBAT) apparatus has a high degree of insulation and a low heating rate that yields onset ignition temperatures very close to the accurate heat-wait-search method used by the extremely well insulated ARC apparatus with several advantages. This paper discusses those advantages (including cost, sampling time, and ability to test multiple samples) and use of the SBAT to determine critical temperatures and material compatibility. Work completed at Safety Management Services, Inc. in collaboration with the Tooele Army Depot and ATK. Presenter’s Biography: Clint Guymon is an engineer at Safety Management Services, Inc. with a doctorate degree in chemical engineering from Brigham Young University. He has experience in Bulk Thermal Stability Characterization via the SBAT Apparatus 2010 Page 2 of 9 molecular dynamics, heat transfer and kinetics modeling, process hazards analysis, and energetic materials testing and classification. Technical Session Paper: Introduction The auto-ignition temperature (AIT) of a substance is not an intrinsic property. A substance can have many different auto-ignition temperatures depending on the environment in which it is found. Specifically, the kinetic parameters (intrinsic properties of the substance) couple with the heat transfer characteristics (defined by the environment or substance configuration) resulting in non-ignition, ignition after a period of time has elapsed, or immediate ignition. The AIT is frequently used to assess the thermal stability of a substance. From this value, storage and transportation assessments are often made. Many different types of devices have been used to determine an auto-ignition temperature of energetic materials including Differential Scanning Calorimeter (DSC), Thermal Gravimetric Analyzer (TGA), Accelerating Rate Calorimeter (ARC), and Simulated Bulk Auto-Ignition Test Apparatus (SBAT). Each of these possesses different heat transfer characteristics and confinement conditions and thus gives different AIT values. This paper discusses the principles that determine the auto-ignition temperature including level of sample insulation, heating rate, confinement, and sample size. We present a simple theoretical model that shows the effects of heating rate, heat transfer, and confinement on the AIT and the time to ignition at a given static temperature. Recent results are also presented comparing the auto-ignition temperature for multiple substances found using the DSC, SBAT, and ARC. We fist discuss the principles that govern the AIT, then the experimental results, and lastly highlight the advantages of the SBAT piece of equipment. Principles Reflected in the Auto-Ignition Temperature Energetic substances are unstable and react with increasing violence as the temperature and pressure are increased. The temperature and pressure are determined by the transfer of heat to and away from the sample and the level of confinement. The transfer of heat can affect the sample temperature resulting in a response in the rate of reaction; likewise, the level of confinement determines the pressure under which the sample reacts. Most energetic materials have a rate of reaction that is strongly dependent on the pressure. The auto-ignition temperature is typically found by placing a sample in a test cell and then raising that temperature while recording the temperature the sample produces significant amounts of heat. As mentioned in the introduction, several variables can significantly affect the value of the auto-ignition temperature. As will be shown (experimentally and theoretically) increasing the heat rate, increasing the level of heat Bulk Thermal Stability Characterization via the SBAT Apparatus 2010 Page 3 of 9 transfer (heat is easily lost from the substance), or reducing the confinement (pressure around sample doesn’t increase during testing) can each result in the increased value of the observed AIT. The sample size affects the level of heat transferred from the substance in that a smaller sample allows for greater heat loss (the resistance to heat loss is reduced). A simple model can be used to easily and independently change the variables mentioned previously and observe the effects. The model is of a sample in a constant volume container (isochoric) where heat can flow into and out of the sample container. The sample reacts according to the Arrhenius equation with a pressure power function. The energy and mass balance equations are given below. Equations are dimensionless to allow for simple comparisons. Parameters used for de-dimensioning are standard temperature, Tθ, for temperature, total mass, m, for mass, and (Cv·m)/h for time (ratio of the product of the constant volume heat capacity and mass to the heat transfer coefficient). Simplifying assumptions were made including constant mass (where one gram of sample reacts to form one gram of gas), sample and gas have the same heat capacity, gas is ideal, and immediate thermal equilibrium exist between sample and gas.
Investigations of dielectric gratings using electrodynamic models based on volume integral equations
Eigenmodes of planar and cylindrical dielectric gratings (DGs) and electromagnetic wave scattering from multiplayer DGs are investigated. The DG characteristics are calculated using numerical-analytical solution of integral equations (IEs).