Modelling non-ideal detonations in commercial explosives
Modelagem de detonações não-ideais de explosivos comerciais
Paulo José Costa Couceiro Júnior, Juan Navarro Miguel
Abstract
Highly non-ideal explosives usually react expressively below their ideal velocities of detonation. In these cases, dimensional effects and product heterogeneities become important to proper model their respective detonation state. Although Direct Numerical Simulation (DNS) techniques can provide a complete and exact solution for this problem, their actual computation cost are still not practical for industrial applications. In order to minimize these constrains, a simplified two-dimensional steady non-ideal detonation model for cylindrical stick explosives is presented. Based on an ellipsoidal shock shape approach (ESSA), the proposed model combines the quasione-dimensional theory for the axial flow solution with the unconfined sonic post-flow conditions at the edge of the explosive. Once calibrated, the model offers the possibility to predict the non-ideal detonation state for any charge diameter, resulting in a full mapping of the diameter-effect curve of the explosive. In addition, the effect of the inert confiner on the detonation flow is calculated by coupling a mechanistic confinement approach with the ESSA model. Thus, the proposed engineering approach is used to model the main properties of one of the most common ammonium nitrate-based explosive used in mining and quarrying industries, including the complete axial flow solution.
Keywords
Resumo
Explosivos altamente não-ideais tendem a reagir com velocidades de detonação expressivamente inferiores às suas velocidades ideais. Nesses casos, os efeitos dimensionais do problema e heterogeneidades dos produtos se tornam fundamentais para realizar, apropriadamente, a modelagem dos seus respectivos estados de detonação. Ainda que as simulações numéricas diretas (DNS) possam prover uma completa e exata solução para esse problema, seu alto custo computacional ainda é um fator restritivo para sua aplicação prática na indústria. A fim de minimizar estas restrições, um modelo de detonação não-ideal estacionário bidimensional para explosivos cilíndricos é desenvolvido. Baseado na aproximação elipsoidal da frente de choque (ESSA), o modelo proposto se fundamenta na teoria quasi-unidimensional para a solução do fluxo reativo axial, combinando o critério de fluxo sônico após o choque com algumas condições limites na borda da carga explosiva. Uma vez calibrado, o modelo oferece a possibilidade de prever o estado não-ideal de detonação em qualquer diâmetro de carga, resultando no mapeamento completo da curva do efeito-diâmetro do explosivo. Adicionalmente, o efeito do material confinante na detonação é calculado ao acoplar uma aproximação mecanicista do confinamento ao modelo ESSA. Portanto, o modelo proposto é usado para modelar as principais propriedades de um dos explosivos baseados em nitrato de amônio mais comuns na indústria mineira e pedreiras, incluindo a completa descrição do fluxo axial.
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Referências
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Submetido em:
09/11/2019
Aceito em:
08/12/2021
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