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

Significance 

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.

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

About the author

Dr. Kun Xue is presently the associate professor in the State Key Laboratory of Explosive science and technology in Beijing Institute of Technology and the head of the safety engineering laboratory. She earned her Ph.D in Mechanical Engineering from Tsinghua University. Since joining Beijing Institute of Technology she has led the Multiphase flow and detonation group and advised 6 Ph.D students and 10 M.S. students.

Dr. Xue’s current research interests are complex compressible multiphase flow, instabilities in shock laden granular flows, multiphase detonation and safety analysis. She has been co-author of two books and more than 30 journal articles and conference proceedings. Her recent work received student best paper awards at CMGM 2021 and 13th NCEM.

She is a committee member of Computational Mechanics of Granular Materials in CSTAM and Physical Gases in CSA. She was awarded the National Science Fund for Excellent Young Scholars in 2021.

About the author

Jiarui Li is currently a 29-year-old Ph.D. student major in Safety Science and Engineering in School of Mechatronical Engineering, Beijing Institute of Technology, China. During his first year as a Ph.D (2019), he has been to the University of Sydney for a half-year exchange and his research is mainly about packing and crystalization of granular materials. Nowadays his focus is on granular-gas interactions in shock driven multiphase flow. Most of his work investigate instability of the interfaces and pressure distribution inside the granular column via the coarse-grained compressible computational fluid dynamics–discrete parcel method (CCFD-DPM) . He has participated in more than ten domestic and international conferences in related fields and made several oral presentations. He won the outstanding student paper award of the Fifth National Conference on Computational Mechanics of Granular Materials (CMGM-2021) as well as the outstanding paper award of the 13th National Conference on Explosion Mechanics (NCEM-2021).

Reference

Li, J., Xue, K., Zeng, J., Tian, B., & Guo, X. (2021). Shock-induced interfacial instabilities of granular mediaJournal of Fluid Mechanics, 930, A22-1-A22-36.

Go To Journal of Fluid Mechanics

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