Modelling spherical explosions with turbulent mixing and post-detonation

Abstract

This paper addresses post detonation modelling in spherical explosions. One of the challenges is thus related to compressible turbulent mixing layers modelling. A one-dimensional flow model is derived consisting in a reduced two-phase compressible flow model with velocity drift. To reduce the number of model parameters, the stiff velocity relaxation limit is considered. A semi-discrete analysis is used resulting in a specific artificial viscosity formulation embedded in the diffuse interface model of Kapila et al. [Phys. Fluids 13(10), 3002–3024 (2001)]10.1063/1.1398042. Thanks to the velocity non-equilibrium model and semi discrete formulation, the model fulfils the second law of thermodynamics in the global sense and uses a single parameter. Multidimensional mixing layer effects occurring at gas-gas unstable interfaces are thus summarized as artificial viscosity effects. Model's predictions are compared against experimental measurements of mixing layer growth in shock tubes at moderate initial pressure ratios as well as fireball radius evolutions in air explosions at high initial pressure ratios. Also, pressure signals recorded at various stations are compared, showing excellent agreement for the leading shock wave as well as the secondary one. With the help of various experiments in the low and high initial pressure ratios bounds, estimates for the interpenetration parameter are given.