A phenomenological drag law in blast-soil interaction

One challenge associated with the simulation of buried detonations involves the treatment of the multiphase flow phenomena related to the soil. At the moment when the soil “shatters” into a dense particulate cloud with detonation products escaping through the soil particles, the continuum model that assumes a single velocity shared by the blast gas and the soil at any given point no longer holds. Instead momentum coupling between the two phases has to be modeled. One characteristic at the stage of soil breaking is that the soil fragments packed in a tight configuration under large pressure provide significant blockage effect characterized by large particle volume fractions. Unfortunately, traditional drag laws do not address the momentum coupling between gas and solid phase under the condition of particle high volume fraction in high speed blast flows. In order to develop a phenomenological drag model to characterize the momentum coupling between the detonation gas and soil fragments when the soil initially breaks into a dense particulate cloud, we conducted a series of numerical simulations on the scale of soil fragments by only considering a small region occupied by a mixture of blast gas and soil fragments (so-called particle-scale simulations). A drag database was constructed based on the drag force collected from the particlescale simulations under the conditions of various soil volume fractions and particle sizes. A new drag law was developed using data regression technique to characterize the dependency of the drag force exerted on particles as a function of particle volume fraction and Reynolds number based on particle size. The proposed drag law provides satisfactory representations of the simulation data, and converge to traditional drag model for isolated particles when the particle volume fraction approaches to zero. Finally, we applied the new phenomenological drag law in the simulations of buried detonation at the stage of soil breaking, and compared the results with the ones from continuum model in which the gas and the soil are assumed moving at the same speed. key word: Drag law, Computational fluid dynamics, Dense particulate flow, Blast wave, Data