Measuring and modelling of pyrotechnic time delay element burn rates

Abstract

Pyrotechnic time delay elements are used in non-electric detonators for blasting operations in the mining and military industries. The improvement of time delay element consistency has been limited by inconsistent measurement techniques, insufficient mathematical models describing the delay element behaviour and physical limitations of the experimental preparation and testing of delay elements. The first part of the investigation focused on finding a solution to the first problem. Currently several techniques have been published and used to measure the burn rates of pyrotechnic delay elements, but each has its own set of problems and limitations. A new method was developed to measure the burn rates of the delay elements using an infrared camera. The average burn rates for a range of compositions were compared to the industrial technique of assembling full detonators and to the commonly used laboratory technique of using two thermocouples. The results showed that the infrared camera method measured slightly lower burn rates than the commercial detonator tests, but higher values than the thermocouple technique. The standard deviations were of the same order in size as those with the full detonators. The thermocouple technique had very large standard deviations, which indicated that the thermocouples used were too large and did not have a fast enough response time. The infrared camera method was found to be reliable for measuring the burn rates of pyrotechnic delay elements. The infrared camera method not only provides a way of measuring the average burn rates, but also gives continuous temperature profile data. The temperature profiles measured for slow-burning delay compositions were found to be fully developed and therefore the average burn rates measured can be assumed to be reliable. The fast-burning delay compositions, on the other hand, had temperature profiles that were not fully developed. These compositions therefore required further modelling in order to confirm that the burn rates measured were accurate. This led to the second part of the investigation, which was to develop a full three-dimensional model of the entire delay element structure. A model was developed using COMSOL Multiphysics software for the slow-burning delay composition of Mn + Sb2O3. The reaction equation was determined through Ekvi thermodynamic simulations, and actual temperature-dependent properties from the literature were used as far as possible. The kinetic parameters were fitted to the infrared camera data to obtain the best-fit kinetics through a least squares method. The Ekvi thermodynamic simulations of the Mn + Sb2O3 composition revealed the formation of a MnSb alloy. This was confirmed using X-ray diffraction analysis of the product residues. The redox reaction of Mn + Sb2O3 was found to undergo a second intermetallic reaction for fuel-rich compositions. The model was also applied to the fast-burning delay composition of Si + Pb3O4. Good agreement between the model and the infrared camera temperature profiles was obtained. The element wall material was found to have a significant impact on the burn rate only when the material thermal conductivity was very high and the volumetric heat capacity was very low. Preheating resulted only for tube materials of diamond and pyrolytic graphite, but no radial combustion was observed. External heat transfer parameters did not have any significant effect on the average burn rate. It was concluded that the ambient temperature, core diameter, volume fraction solids, wall thickness and heat of reaction are the factors that most significantly influence the average burn rate of the compositions.