Linear stability of particle laden flows: the influence of added mass, fluid acceleration and Basset history force

Klinkenberg, Joy; Lange, de Hc Rick; Brandt, Luca

doi:10.1007/s11012-013-9828-2

Cited by 17 publications

(6 citation statements)

References 38 publications

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“…Other terms in the particle momentum equation (see Maxey & Riley 1983) are neglected since they remain small compared with drag when the density ratio r 1. These neglected terms are also found to have less effect on the stability analysis in relatively low Reynolds number turbulence as demonstrated by Klinkenberg et al (2014). Particle-particle collisions are not taken into consideration due to the low volume concentrations, and we exert a purely elastic collision between particles and the upper/lower walls.…”

Section: Methodsmentioning

confidence: 90%

Modulation of the turbulence regeneration cycle by inertial particles in planar Couette flow

Wang

Richter

2018

J. Fluid Mech.

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Two-way coupled direct numerical simulations are used to investigate the effects of inertial particles on self-sustained, turbulent coherent structures (i.e. the so-called the regeneration cycle) in plane Couette flow at low Reynolds number just above the onset of transition. Tests show two limiting behaviors with increasing particle inertia, similar to the results from the linear stability analysis of Saffman (1962): low-inertia particles trigger the laminar-to-turbulent instability whereas high-inertia particles tend to stabilize turbulence due to the extra dissipation induced by particle-fluid coupling. Furthermore, it is found that the streamwise coupling between phases is the dominant factor in damping the turbulence and is highly related to the spatial distribution of the particles. The presence of particles in different turbulent coherent structures (large scale vortices or large scale streaks) determines the turbulent kinetic energy of particulate phase, which is related to the particle response time scaled by the turnover time of large scale vortices. By quantitatively investigating the periodic character of the whole regeneration cycle and the phase difference between linked sub-steps, we show that the presence of inertial particles does not alter the periodic nature of the cycle or the relative length of each of the sub-steps. Instead, high-inertia particles greatly weaken the large-scale vortices as well as the streamwise vorticity stretching and lift-up effects, thereby suppressing the fluctuating amplitude of the large scale streaks. The primary influence of low-inertia particles, however, is to strengthen the large scale vortices, which fosters the cycle and ultimately reduces the critical Reynolds number.

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Section: Methodsmentioning

confidence: 90%

Modulation of the turbulence regeneration cycle by inertial particles in planar Couette flow

Wang

Richter

2018

J. Fluid Mech.

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“…The modal and non-modal stability of small spherical particles of density of the order of that of the fluid is reported in Klinkenberg et al (2013a). Here, the Stokes drag, added mass and fluid acceleration are used to describe the interactions with the fluid.…”

Section: Channel Flow With Small Particlesmentioning

confidence: 99%

The lift-up effect: The linear mechanism behind transition and turbulence in shear flows

Brandt

2014

European Journal of Mechanics - B/Fluids

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145

126

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The formation and amplification of streamwise velocity perturbations induced by cross-stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so neatly identified by Ellingsen and Palm in 1975, is a key process in transition to turbulence and self-sustained turbulence. In this review, we first present the original derivation and early studies and then discuss the non-modal growth of streaks, the result of the lift-up process, in transitional and turbulent shear flows. In the second part, the effects on the lift-up process of additives in the fluid and of a second phase are discussed and new results presented with emphasis on particle-laden shear flows. For all cases considered, we see the lift-up process to be a very robust process, always present as a first step in subcritical transition.

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“…In our previous work [13,14], the linear stability of flows seeded with either heavy or light particles was investigated. For a flow with heavy particles only, the Stokes drag needs to be taken into account.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of laminar-turbulent transition in particle-laden channel flow

et al. 2013

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We present direct numerical simulations of subcritical transition to turbulence in a particle-laden channel flow, with particles assumed rigid, spherical, and heavier than the fluid. The equations describing the fluid flow are solved with an Eulerian mesh, whereas those describing the particle dynamics are solved by Lagrangian tracking. Two-way coupling between fluid and particles is modeled with Stokes drag. The numerical code is first validated against previous results from linear stability: the nonmodal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for linear disturbance amplification at subcritical conditions as for the case of a single phase fluid. To analyze the full nonlinear transition, we examine two scenarios well studied in the literature: (1) transition initiated by streamwise independent counter-rotating streamwise vortices and one three-dimensional mode and (2) oblique transition, initiated by the nonlinear interaction of two symmetric oblique waves. The threshold energy for transition is computed, and it is demonstrated that for both scenarios the transition may be facilitated by the presence of particles at low number density. This is due to the fact that particles may introduce in the system detrimental disturbances of length scales not initially present. At higher concentrations, conversely, we note an increase of the disturbance energy needed for transition. The threshold energy for the oblique scenario shows a more significant increase in the presence of particles, by a factor about four. Interestingly, for the streamwise-vortex scenario the time at which transition occurs increases with the particle volume fraction when considering disturbances of equal initial energy. These results are explained by considering the reduced amplification of oblique modes in the two-phase flow. The results from these two classical scenarios indicate that, although linear stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown. These effects can be responsible of the reduced drag observed in turbulent channel flow laden with heavy particles.

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Linear stability of particle laden flows: the influence of added mass, fluid acceleration and Basset history force

Cited by 17 publications

References 38 publications

Modulation of the turbulence regeneration cycle by inertial particles in planar Couette flow

Modulation of the turbulence regeneration cycle by inertial particles in planar Couette flow

The lift-up effect: The linear mechanism behind transition and turbulence in shear flows

Numerical study of laminar-turbulent transition in particle-laden channel flow

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