Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows

The exact regularised point particle (ERPP) method is extended to treat the inter-phase momentum coupling between particles and fluid in the presence of walls by accounting for vorticity generation due to particles close to solid boundaries. The ERPP method overcomes the limitations of other methods by allowing the simulation of an extensive parameter space (Stokes number, mass loading, particle-to-fluid density ratio and Reynolds number) and of particle spatial distributions that are uneven (few particles per computational cell). The enhanced ERPP method is explained in detail and validated by considering the global impulse balance. In conditions when particles are located close to the wall, a common scenario in wall-bounded turbulent flows, the main contribution to the total impulse arises from the particle-induced vorticity at the solid boundary. The method is applied to direct numerical simulations of particle-laden turbulent pipe flow in the two-way coupling regime to address turbulence modulation. The effects of the mass loading, the Stokes number and the particle-to-fluid density ratio are investigated. The drag is either unaltered or increased by the particles with respect to the uncoupled case. No drag reduction is found in the parameter space considered. The momentum stress budget, which includes an extra stress contribution by the particles, provides the rationale behind the drag behaviour. The extra stress produces a momentum flux towards the wall that strongly modifies the viscous stress, the culprit of drag at solid boundaries.

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Sedimentation of finite-size spheres in quiescent and turbulent environments

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.698 ◽

2016 ◽

Vol 788 ◽

pp. 640-669 ◽

Cited By ~ 49

Author(s):

Walter Fornari ◽

Francesco Picano ◽

Luca Brandt

Keyword(s):

Turbulent Flow ◽

Settling Velocity ◽

Solid Phase ◽

Density Ratio ◽

Finite Size ◽

Spherical Particles ◽

Volume Fractions ◽

Turbulent Environments ◽

The Mean ◽

Quiescent Fluid

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

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Modulation of isotropic turbulence by particles of Taylor length-scale size

Journal of Fluid Mechanics ◽

10.1017/s0022112009994022 ◽

2010 ◽

Vol 650 ◽

pp. 5-55 ◽

Cited By ~ 154

Author(s):

FRANCESCO LUCCI ◽

ANTONINO FERRANTE ◽

SAID ELGHOBASHI

Keyword(s):

Isotropic Turbulence ◽

Volume Fraction ◽

Density Ratio ◽

Particle Diameter ◽

Finite Size ◽

Rate Of Change ◽

Spherical Particles ◽

Length Scale ◽

Frequency Spectra ◽

Scale Size

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤d/λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤d/η≤35 and 38≤τp/τk≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φm≤1.0, corresponding to a volume fraction of 0.01≤φv≤0.1 and density ratio of 2.56≤ρp/ρf≤10. The maximum number of dispersed particles is 6400 for φv=0.1. The typical particle Reynolds number is of O(10). The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate (t), its two-way coupling rate of change Ψp(t) and frequency spectra E(ω) are discussed.In contrast to particles with d < η, the effect of the particles in this study, with d > η, is that E(t) is always smaller than that of the single-phase flow. In addition, Ψp(t) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.

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Improved Discrete Random Walk Stochastic Model for Simulating Particle Dispersion and Deposition in Inhomogeneous Turbulent Flows

Journal of Fluids Engineering ◽

10.1115/1.4047538 ◽

2020 ◽

Vol 142 (10) ◽

Author(s):

Amir A. Mofakham ◽

Goodarz Ahmadi

Keyword(s):

Random Walk ◽

Turbulent Flows ◽

Particle Deposition ◽

Finite Size ◽

Particle Dispersion ◽

Concentration Profiles ◽

Velocity Fluctuations ◽

Point Particles ◽

Deposition Velocities ◽

Gradient Drift

Abstract The performance of different versions of the discrete random walk models in turbulent flows with nonuniform normal root-mean-square (RMS) velocity fluctuations and turbulence time scales were carefully investigated. The OpenFOAM v2−f low Reynolds number turbulence model was used for evaluating the fully developed streamwise velocity and the wall-normal RMS velocity fluctuations profiles in a turbulent channel flow. The results were then used in an in-house matlab particle tracking code, including the drag and Brownian forces, and the trajectories of randomly injected point-particles with diameters ranging from 10 nm to 30 μm were evaluated under the one-way coupling assumption. The distributions and deposition velocities of fluid-tracer and finite-size particles were evaluated using the conventional-discrete random walk (DRW) model, the modified-DRW model including the velocity gradient drift correction, and the new improved-DRW model including the velocity and time gradient drift terms. It was shown that the conventional-DRW model leads to superfluous migration of fluid-point particles toward the wall and erroneous particle deposition rate. The concentration profiles of tracer particles obtained by using the modified-DRW model still are not uniform. However, it was shown that the new improved-DRW model with the velocity and time scale drift corrections leads to uniform distributions for fluid-point particles and reasonable concentration profiles for finite-size heavy particles. In addition, good agreement was found between the estimated deposition velocities of different size particles by the new improved-DRW model with the available data.

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Lagrangian frequency spectra of vertical velocity and vorticity in high-Reynolds-number oceanic turbulence

Journal of Fluid Mechanics ◽

10.1017/s0022112098008787 ◽

1998 ◽

Vol 362 ◽

pp. 177-198 ◽

Cited By ~ 40

Author(s):

REN-CHIEH LIEN ◽

ERIC A. D'ASARO ◽

GEOFFREY T. DAIRIKI

Keyword(s):

Turbulent Flows ◽

Frequency Spectrum ◽

Finite Size ◽

Inertial Subrange ◽

Substantial Part ◽

Spatial Average ◽

Vertical Acceleration ◽

Frequency Range ◽

Frequency Spectra ◽

Large Eddy

Lagrangian properties of oceanic turbulent boundary layers were measured using neutrally buoyant floats. Vertical acceleration was computed from pressure (depth) measured on the floats. An average vertical vorticity was computed from the spin rate of the float. Forms for the Lagrangian frequency spectra of acceleration, ϕa(ω), and the Lagrangian frequency spectrum of average vorticity are found using dimension analysis. The flow is characterized by a kinetic energy dissipation rate, ε, and a large-eddy frequency, ω0. The float is characterized by its size. The proposed non-dimensionalization accurately collapses the observed spectra into a common form. The spectra differ from those expected for perfect Lagrangian measurements over a substantial part of the measured frequency range owing to the finite size of the float. Exact theoretical forms for the Lagrangian frequency spectra are derived from the corresponding Eulerian wavenumber spectra and a wavenumber–frequency distribution function used in previous numerical simulations of turbulence. The effect of finite float size is modelled as a spatial average. The observed non-dimensional acceleration and vorticity spectra agree with these theoretical predictions, except for the high-frequency part of the vorticity spectrum, where the details of the float behaviour are important, but inaccurately modelled. A correction to the exact Lagrangian acceleration spectra due to measurement by a finite-sized float is thus obtained. With this correction, a frequency range extending from approximately one decade below ω0 to approximately one decade into the inertial subrange can be resolved by the data. Overall, the data are consistent with the proposed transformation from the Eulerian wavenumber spectrum to the Lagrangian frequency spectrum. Two parameters, ε and ω0, are sufficient to describe Lagrangian spectra from several different oceanic turbulent flows. The Lagrangian Kolmogorov constant for acceleration, βa≡ϕa/ε, has a value between 1 and 2 in a convectively driven boundary layer. The analysis suggests a Lagrangian frequency spectrum for vorticity that is white at all frequencies in the inertial subrange and below, and a Lagrangian frequency spectrum for energy that is white below the large-eddy scale and has a slope of −2 in the inertial subrange.

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Reduced particle settling speed in turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.648 ◽

2016 ◽

Vol 808 ◽

pp. 153-167 ◽

Cited By ~ 17

Author(s):

Walter Fornari ◽

Francesco Picano ◽

Gaetano Sardina ◽

Luca Brandt

Keyword(s):

Solid Phase ◽

Density Ratio ◽

Mean Square Displacement ◽

Particle Diameter ◽

Finite Size ◽

Mean Square ◽

Rigid Spheres ◽

The Mean ◽

Settling Speed ◽

Quiescent Fluid

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).

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Vortex-induced vibration of a prism in internal flow

Journal of Fluid Mechanics ◽

10.1017/s0022112009991893 ◽

2009 ◽

Vol 641 ◽

pp. 431-440 ◽

Cited By ~ 11

Author(s):

M. SÁNCHEZ-SANZ ◽

A. VELAZQUEZ

Keyword(s):

Critical Mass ◽

Density Ratio ◽

Internal Flow ◽

Reynolds Numbers ◽

Fluid Density ◽

Structural Damping ◽

Mass Ratio ◽

Transitional Regime ◽

Restoring Force ◽

Irregular Pattern

In this article, we study the influence of solid-to-fluid density ratio m on the type of vortex-induced oscillation of a square section prism placed inside a two-dimensional channel. We assume that the solid body has neither structural damping nor spring restoring force. Accordingly, the prism equation of motion contains only inertia and aerodynamics forces. The problem is considered in the range of Reynolds numbers Re ∈ [50 200] (based on the prism cross-section height h) and channel widths H = H′/h ∈ [2.5 10]. We found that, for each Re and H, there is a critical mass ratio mc that separates two different oscillation regimes. For m > mc, the prism oscillation is periodical and contains a single harmonic. For m < mc, the prism oscillation changes completely and assumes an irregular pattern that is characterized by multiple harmonics that appear to belong to a uniform spectrum. The change from one regime to the other is abrupt and we were not able to observe a transitional regime in which the number of response harmonics grew by finite steps. The value of the critical mass ratio grows along with the Reynolds number and the channel width.

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Turbulent Clustering of Point Particles and Finite-Size Particles in Isotropic Turbulent Flows

Industrial & Engineering Chemistry Research ◽

10.1021/ie303507d ◽

2013 ◽

Vol 52 (33) ◽

pp. 11294-11301 ◽

Cited By ~ 4

Author(s):

Guodong Jin ◽

Yun Wang ◽

Jian Zhang ◽

Guowei He

Keyword(s):

Turbulent Flows ◽

Finite Size ◽

Point Particles

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New class of turbulence in active fluids

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1509304112 ◽

2015 ◽

Vol 112 (49) ◽

pp. 15048-15053 ◽

Cited By ~ 60

Author(s):

Vasil Bratanov ◽

Frank Jenko ◽

Erwin Frey

Keyword(s):

Turbulent Flows ◽

Stokes Equations ◽

Spatial Scales ◽

Finite Size ◽

Power Laws ◽

Theoretical Work ◽

Navier Stokes ◽

Physical Parameters ◽

New Class ◽

General Terms

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

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