Pressure evolution in shock-compacted granular media

The pressure evolution associated with the transient shock-induced infiltration of gas flow through granular media consisting of mobile particles is numerically investigated using a coupled Eulerian–Lagrangian approach. The coupling between shock compaction and interstitial flow has been revealed. A distinctive two-stage diffusing pressure field with deflection occurring at the tail of the compaction front is found, with corresponding spikes in both gaseous velocity and temperature profiles emerging within the width of the compaction front. The compaction front, together with the deflection pressure, reaches a steady state during the later period. An analytical prediction of the steady deflection pressure that considers the contributions of porosity and the non-isothermal effect is proposed. The isothermal single-phase method we developed, combining the porosity jump condition across the compaction front, shows consistent pressure evolution with the non-isothermal CMP-PIC one under weak shock strength and low column permeability. Lastly, the microscale mechanism governing the formation of not only pressure deflection but also gaseous velocity and temperature spikes within the width of the compaction front has been described. These aforementioned evolutions of the flow field are shown to arise from the nozzling effects associated with the particle-scale variations in the volume fraction.