Fully resolved simulation of a shockwave interacting with randomly clustered particles via a ghost-cell immersed boundary method

Fully resolved direct numerical simulations are performed to investigate the interaction between a planar shockwave and 300 randomly clustered particles. The particle interfaces are captured with the ghost-cell immersed boundary method. Four cases of different shock Mach numbers up to 6.0 are investigated with a relatively high volume fraction of 14.7% of clustered particles. Results show that the reflected shocks form a planar shockwave propagating upstream, with its velocity decreasing with the increase in Mach number. In small Mach number cases, the transmitted shock remains planar and exceeds its original propagating speed. In high Mach number cases, the transmitted shock is highly curved and slowed down. The peak drag coefficients of all particles could exhibit a linear correlation with the streamwise location. The lift force coefficients could become similar to or even larger than the drag coefficients when the particles reside in post-shock regions. The peak lift force coefficients are the smallest for the first and last rows, and highest in the first half part of clusters, which is due to different mechanisms. The transverse effects of shock–cluster interaction are stronger in higher Mach number cases. This result indicates that the transverse force could not be ignored in a particle cluster with a relatively high volume fraction, especially when the Mach number is high. Fluctuating flow quantities indicate that the increase in Mach number could enhance the fluctuations in the transverse direction and reduce the streamwise mean velocity, resulting in stronger fluctuating fields compared with the mean flows.