Transient instability in long, tilted water columns with fast-settling, particle-laden layers
Journal
Journal of Fluid Mechanics
Journal Volume
929
Date Issued
2021
Author(s)
Abstract
We study the stability of unsteady particle-laden flows in long, tilted water columns in batch settling mode, where the quasi-steady assumption of base flow no longer holds for the fast settling of particles. For this purpose, we introduce a settling time scale in the momentum and transport equations to solve the unsteady base flow, and utilise non-modal analysis to examine the stability of the disturbance flow field. The base flow increases in magnitude as the settling speed decreases and attains its maximum value when the settling speed becomes infinitesimal. The time evolution of the disturbance flow energy experiences an algebraic growth caused by the lift-up mechanism of the wall-normal disturbance, followed by an exponential growth owing to the shear instability of the base flow. The streamwise and spanwise wavenumbers corresponding to the peak energy gain are identified for both stages. In particular, the flow instability is enhanced as the Prandtl number increases, which is attributed to the sharpening of the particle-laden interface. On the other hand, the flow instability is suppressed by the increase in settling speed, because less disturbance energy can be extracted from the base flow. There exists an optimal tilted angle for efficient sedimentation, where the particle-laden flow is relatively stable and is accompanied by a smaller energy gain of the disturbance. ?
Subjects
shear-flow instability
Aerodynamics
Modal analysis
Prandtl number
Stability
Baseflows
Energy gain
Flow instabilities
Particle laden flows
Particle-laden
Settling particles
Settling speed
Shear-flow instability
Transient instability
Water columns
Shear flow
flow field
flow modeling
flow stability
fluid dynamics
numerical model
shear flow
unsteady flow
wave force
Type
journal article