Abstract
This study focuses on the effects of a large Stokes number (St) on the perturbation growth in linear and nonlinear stages of a Richtmyer–Meshkov instability (RMI) in a gas-particle system, which to the best of our knowledge has not been previously reported. A linear growth model is developed by linear stability analysis and numerically verified by the compressible multiphase particle-in-cell (CMP-PIC) method. Additionally, the RMI growth characteristics in the nonlinear stage are also investigated by CMP-PIC. For the linear growth model, two major differences characterize the effects of a large St. The first one is that an RMI with a large St, which performs significantly different from the RMI with a small St, is induced and driven only by the density difference of the gas-phase and totally independent of particle density. Second, due to the significant momentum coupling effects between gas and particle phases, which govern the gas-particle flow, the growth rate experiences exponential decay, even in the linear RMI stage. The decay behavior performs markedly different from any previous RMI models, especially those of the original single-phase RMI and the gas-particle RMI with a small St. Notably, in the nonlinear stage of the RMI with a large particle volume fraction, the decay effects are much more pronounced and lead to a fall in the growth rate to almost zero, which is not found in any other type of RMI. These findings offer the possibility to develop a new method to control the development of hydrodynamic instability.
Highlights
Shock-driven multiphase flows, such as that in a gas-particle system, often occur in studies involving the Richtmyer–Meshkov instability (RMI) phenomenon,1–4 such as in supernova (SN) explosions,5 particle imaging velocimetry (PIV) measurements,6–9 and inertial confinement fusion (ICF),10,11 for which one of the critical issues is to suppress the hydrodynamic instability
For the dilute gas-particle RMI issue, the growth rate can be simplified by combining Eqs. (20a) and (18), and the growth rate for a dilute pattern can be predicted as dh dt
The results demonstrated that the growth rate of the dilute pattern in the early stage of the linear regime behaved the same and was independent of the volume fraction value of the particle phases
Summary
Shock-driven multiphase flows, such as that in a gas-particle system, often occur in studies involving the Richtmyer–Meshkov instability (RMI) phenomenon, such as in supernova (SN) explosions, particle imaging velocimetry (PIV) measurements, and inertial confinement fusion (ICF), for which one of the critical issues is to suppress the hydrodynamic instability. Of the multiphase RMI were mainly conducted on the gas-particle system with a small St. For region A in Fig. 1 (0 < αp < 0.01 and St ≪ 1), numerous studies have been conducted on theoretical modeling and numerical verification of the linear growth rate for the gas-particle flow.. A uniform multiphase Atwood model, ADm, which was applicable to both the dilute and dense gas-particle flow, was developed in our previous study.. Ukai et al. conducted a numerical simulation for the dilute gas-particle flow with a large St, and their results showed that the RMI growth rate agreed well with that in the original Richtmyer’s model..
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