A Richtmyer–Meshkov instability analog in granular materials with distinct nature

Fingering/jetting instabilities of dense granular media emanate from destabilized granular surfaces affected by shock waves. They generally have fundamental impacts on several engineering processes and natural phenomena, particularly on volcanic eruptions and supernova explosions. It is well known that when particle fingers protrude into gases, heavy fluid reminiscent thrust into a light fluid produced by Richtmyer–Meshkov instability (RMI). This phenomenon has inspired researchers to recognize and identify the potential differences between the RMI and shock-driven particle jetting behavior. For instance, it was revealed that the occurrence of jetting instability of particles that have been mixed with gases and dispersed explosively is attributed to shock-driven multiphase instability (SDMI), a RMI variant produced by the perturbed interface of multiphase fluid mixtures accelerated by shock effects.

SDMI evolution is characterized shorter equilibrium between gases and particles compared with the characteristics hydrodynamic time scale. Thus, a low particle volume fraction is recommended for efficient SDMI evolution. However, this does not apply to interfacial instabilities of dense granular media like those observed in experiments involving closely packed shock-loaded particles. Hence, the interfacial instability produced by interfacial granular flows is referred to as shock-driven granular instability (SDGI).

Unlike SDMI and RMI, SDGI initiation needs to satisfy a particular instability criterion that is often assumed to be equal to the Drucker–Prager yield criterion. However, issues have been raised on the validity of this assumption due to the non-equilibrium and transient coupling between the particle and interstitial gas-phase associated with the continuum approximation of granular materials. Therefore, a thorough understanding of the interactions between interstitial flows and particles, particles and shock and interactions amongst the particles could provide more insights into SDGI.

On this account, PhD candidate Jiarui Li, Professor Kun Xue and Professor Baolin Tian from Beijing Institute of Technology in collaboration with Dr. Junsheng Zeng from Peng Cheng Laboratory and Professor Xiaohu Guo from Daresbury Laboratory investigated the shock-induced instability of the gases-dense granular media interface with finite length using the coarse-grained compressible computational fluid dynamics–discrete parcel method (CCFD-DPM). The main aim was to provide a thorough understanding of the underlying physics and perturbation growth law of SDGIs in a more general fashion characterized by persistent coupling between the particles and shock-induced flows. Their work is currently published in the Journal of Fluid Mechanics.

The research team established that the SDGI is governed by distinctly different mechanisms even though it generated a spike-bubble structure reminiscent similar to that of RMI. In contrast with RMI, which arises from the deposition of baroclinic vorticity on the interface, SDGI emanates from the interfacial granular flows caused by the transient coupling between the particles and gas flows. In addition, the SDGI obeyed different growth laws from those of SDMI and RMI. The growth regimes were characterized by semilinear slow growth regime, exponentially accelerated growth regime and quadratic asymptotic growth regime. These regimes resulted in growth curves that corresponded to the dominant underlying mechanisms of SDGI. Furthermore, an SDGI instability criterion was established for granular media with finite and infinite lengths.

In summary, the researchers provided a detailed understanding of SDGI, a relatively new shock-induced interfacial instability with unique growth criterion and perturbation growth laws. Theoretical models were further developed to predict the upper growth rate limit and characteristic growth rate during the initial and third stages, respectively. A scaling growth law was also derived by normalizing the time using the rarefaction propagation time and considering the perturbation effects and shock strength. In a statement to Advances in Engineering, Professor Kun Xue, the corresponding author explained their study provided valuable insights into the transient multiphase flows of complicated wave spectra and related interfacial instabilities.