Analogues of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in flows with nonuniform particle and droplet seeding

Abstract

The well-known Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities characterize the behavior of flows where two gases (or fluids) of different densities mix due to gravity (RT) or due to impulsive acceleration (RM). Recently, analogous instabilities have been observed in two-phase flows where the seeding density of the second phase, e.g., particles or droplets in gas, and the resulting average density, is initially non-uniform. The forcing causes the second phase to move with respect to the embedding medium. With sufficient seeding concentration, this leads to entrainment of the embedding phase. The resulting movement is similar to the movement that would evolve in a mixing flow with no second phase seeding, but with non-uniform density (not unlike a mixture of lighter and heavier gases), where RT and RM instabilities develop in the case of gravityinduced and impulsive acceleration, respectively. The hydrocode SHAMRC has been used in the past to study the formation and growth of the RM instability. Here we attempt to use it to model the first order formation and growth phenomena of the new class of instability in two-phase flows first, by approximating the second phase as a continuous fluid with an averaged density, and second, by taking the relative motion of particles (droplets) into account explicitly. The initial conditions are varied to provide a wide range of instability growth rates. Comparison of the numerical results with experiment shows good agreement.

Instabilities in a shock interaction with a perturbed curtain of particles

“…In this paper, we study the interaction between a moving, normal shock and a perturbed curtain of particles. We show that the curtain exhibits instabilities that are very similar to RMI and RTI, however, as earlier research [8,9] indicates, these instabilities are non-baroclinic, but rather driven by interphase velocities and changes in number density in the particle phase. Here and further on, 'interphase velocity' refers to a velocity difference between the gaseous and particle phases.…”

Formation of a falling particle curtain

“…One earlier study was also conducted for the multiphase analogue of RTI [5] for A m ~ 0.03. For the flow under investigation (air with a small volume fraction of micron-sized glycol droplets), it was concluded that morphologically and in terms of instability growth, the results were indistinguishable from classical single-phase RTI, with droplet seeding effectively contributing only to local average density.…”

Morphology of shock-accelerated multiphase flow: experiment and modeling

“…Similar problems of interest (shock propagation through a combination of gases and non-gaseous inclusions) include coal dust explosions [3], supersonic combustion with fuel droplets [4], an interstellar gas or plasma with dust particles [5], and inertial confinement fusion (ICF) [6]. Far from behaving as passive tracers following the flow, particles or droplets can actually cause instability in the fluid after shock passage: this recently identified phenomenon is called a particle-lag instability (PLI) [7,8]. It occurs due to variations in the average density resulting from nonuniform initial distribution of the non-gaseous phase.…”

“…One of the primary purposes of our experiments is to establish quantitative benchmarks for validation of numerical techniques. The authors have reported direct comparison of the experiments with simulations preformed with a multiphase code SHAMRC [8,9,10]. Anderson et al [10] demonstrated that careful modeling of initial conditions is required to reproduce experimental results.…”