Numerical study of particle-induced Rayleigh-Taylor instability: Effects of particle settling and entrainment

Abstract

In this study, we investigate Rayleigh-Taylor instability in which the density stratification is caused by the suspension of particles in liquid flows using the conventional single-phase model and Euler-Lagrange (EL) two-phase model. The single-phase model is valid only when the particles are small and number densities are large, such that the continuum approximation applies. The present single-phase results show that the constant settling of the particle concentration restricts the lateral development of the vortex ring, which results in a decrease of the rising speed of the Rayleigh-Taylor bubbles. The EL model enables the investigation of particle-flow interaction and the influence of particle entrainment, resulting from local non-uniformity in the particle distribution. We compare bubble dynamics in the single-phase and EL cases, and our results show that the deviation between the two cases becomes more pronounced when the particle size increases. The main mechanism responsible for the deviation is particle entrainment, which can only be resolved in the EL model. We provide a theoretical argument for the small-scale local entrainment resulting from the local velocity shear and non-uniformity of the particle concentration. The theoretical argument is supported by numerical evidence. Energy budget analysis is also performed and shows that potential energy is released due to the interphase drag and buoyant effect. The buoyant effect, which results in the transformation of potential energy into kinetic energy and shear dissipation, plays a key role in settling enhancement. We also find that particle entrainment increases the shear dissipation, which in turn enhances the release of potential energy.

Formation of drops and rings in double-diffusive sedimentation

“…In Chou et al (2015), calculation of Lagrangian particles was validated by some canonical cases of suspended sediment transport. The present EL model has been applied to study particle-induced RTI (Chou & Shao 2016). In this study, following Chou & Shao (2016), direct numerical simulation and point-force representation for fine suspended particles are employed to study double-diffusive sedimentation.…”

Numerical study of double-diffusive sedimentation in thermally stratified fluid

“…Chou et al (2015) validated the calculation of Lagrangian particles by some canonical cases of suspended sediment transport. The present Eulerian-Lagrangian model has been applied to study particle-induced Rayleigh-Taylor instability (Chou & Shao 2016), convective sedimentation in a sharp density interface (Shao, Hung & Chou 2017) and enhanced sedimentation in inclined water columns (Chang et al 2019).…”

“…Here, for the sake of simplicity, we focus only on cases with φ * 0 = 8.4 × 10 −4 , but the findings will also be applied to cases with a lower φ * 0 . Following Chou & Shao (2016), if both phases are static in the initial state, the energy budget of the present Eulerian-Lagrangian system for a horizontally periodic domain at time t = t is obtained from a combination of the inner product of u c to the momentum equations of the continuum phase (2.16) and the inner product of u p,k to . Time histories of the (dimensionless) fluctuation flux w c φ at both the centre (z = 0) and the lower bound of the thermally controlled region in cases corresponding to figure 5(a-c).…”

“…the momentum equation of the particle phase. As detailed in Chou & Shao (2016), the resulting dimensionless equation for energy budget can be written as…”

Numerical Study of Turbidity Current over a Three-Dimensional Seafloor

“…Their numerical simulations have revealed more detailed features of particle-laden flow concerning front location and deposited mass. For more information about the theoretical formulation and application of two-way coupled Euler-Lagrange models, one can refer to [11,12]. Large Eddy Simulation (LES) is applied to study the evolution of gravity currents and its interaction with structures on complex 3-D seafloors under high Reynolds number conditions [13].…”