Effect of Domain Size on Fluid–Particle Statistics in Homogeneous, Gravity-Driven, Cluster-Induced Turbulence

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Volume Fraction ◽  
Finite Size ◽  
Domain Size ◽  
Spatial Filter ◽  
High Mass ◽  
Inertial Particles ◽  
Spatially Correlated ◽  
Gravity Driven ◽  
Adaptive Spatial Filter ◽  
Particle Statistics

Scaling of volume fraction and velocity fluctuations with domain size is investigated for high-mass-loading suspensions of finite-size inertial particles subject to gravity. Results from highly resolved Euler–Lagrange simulations are evaluated via an adaptive spatial filter with an averaging volume that varies with the local particle concentration. This filter enables the instantaneous particle velocity to be decomposed into a spatially correlated contribution used in defining the particle-phase turbulent kinetic energy (TKE), and a spatially uncorrelated contribution used in defining the granular temperature. The total granular energy is found to grow nearly linearly with the domain size, while the balance between the separate contributions remains approximately constant.

On fluid–particle dynamics in fully developed cluster-induced turbulence

2015 ◽  
Vol 780 ◽  
pp. 578-635 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Kinetic Energy ◽  
Volume Fraction ◽  
Finite Size ◽  
Fluid Phase ◽  
Particle Phase ◽  
Pressure Tensor ◽  
Production Term ◽  
Velocity Statistics ◽  
Gravity Driven ◽  
Momentum Coupling

At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

Numerical study of collisional particle dynamics in cluster-induced turbulence

2014 ◽  
Vol 747 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Velocity Field ◽  
Volume Fraction ◽  
Numerical Study ◽  
Computational Study ◽  
Finite Size ◽  
Fluid Phase ◽  
Spatial Filter ◽  
Particle Dynamics ◽  
Spatial Correlations ◽  
Phase Volume Fraction

AbstractWe present a computational study of cluster-induced turbulence (CIT), where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. A separation of length scales must be established when evaluating the particle dynamics in order to distinguish between the continuous mesoscopic velocity field and the uncorrelated particle motion. To accomplish this, an adaptive spatial filter is employed on the Lagrangian data with an averaging volume that varies with the local particle-phase volume fraction. This filtering approach ensures sufficient particle sample sizes in order to obtain meaningful statistics while remaining small enough to avoid capturing variations in the mesoscopic particle field. Two-point spatial correlations are computed to assess the validity of the filter in extracting meaningful statistics. The method is used to investigate, for the first time, the properties of a statistically stationary gravity-driven particle-laden flow, where particle–particle and fluid–particle interactions control the multiphase dynamics. Results from fully developed CIT show a strong correlation between the local volume fraction and the granular temperature, with maximum values located at the upstream boundary of clusters (i.e. where maximum compressibility of the particle velocity field exists), while negligible particle agitation is observed within clusters.

scholarly journals Evolution of Shape and Volume Fraction of Superconducting Domains with Temperature and Anion Disorder in (TMTSF)2ClO4

Crystals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 72
Author(s):  
Kaushal K. Kesharpu ◽  
Vladislav D. Kochev ◽  
Pavel D. Grigoriev
Keyword(s):  
Cooling Rate ◽  
Annealing Time ◽  
Volume Fraction ◽  
Density Wave ◽  
Spin Density Wave ◽  
Finite Size ◽  
Organic Superconductors ◽  
Organic Superconductor ◽  
Sample Length ◽  
Sample Shape

In highly anisotropic organic superconductor (TMTSF)2ClO4, superconducting (SC) phase coexists with metallic and spin-density wave phases in the form of domains. Using the Maxwell-Garnett approximation (MGA), we calculate the volume ratio and estimate the shape of these embedded SC domains from resistivity data at various temperature and anion disorder, controlled by the cooling rate or annealing time of (TMTSF)2ClO4 samples. We found that the variation of cooling rate and of annealing time affect differently the shape of SC domains. In all cases the SC domains have oblate shape, being the shortest along the interlayer z-axis. This contradicts the widely assumed filamentary superconductivity along the z-axis, used to explain the anisotropic superconductivity onset. We show that anisotropic resistivity drop at the SC onset can be described by the analytical MGA theory with anisotropic background resistance, while the anisotropic Tc can be explained by considering a finite size and flat shape of the samples. Due to a flat/needle sample shape, the probability of percolation via SC domains is the highest along the shortest sample dimension (z-axis), and the lowest along the sample length (x-axis). Our theory can be applied to other heterogeneous superconductors, where the size d of SC domains is much larger than the SC coherence length ξ, e.g., cuprates, iron-based or organic superconductors. It is also applicable when the spin/charge-density wave domains are embedded inside a metallic background, or vice versa.

Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics

2017 ◽  
Vol 814 ◽  
pp. 592-613 ◽  
Author(s):  
Andras Nemes ◽  
Teja Dasari ◽  
Jiarong Hong ◽  
Michele Guala ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Response Times ◽  
Field Measurements ◽  
Stokes Number ◽  
Inertial Particles ◽  
Natural Setting ◽  
Scale Particle ◽  
Particle Imaging

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

Particle-Laden Turbulence: Progress and Perspectives

2021 ◽  
Vol 54 (1) ◽  
Author(s):  
Luca Brandt ◽  
Filippo Coletti
Keyword(s):  
Fluid Dynamics ◽  
Fluid Mechanics ◽  
Online Publication ◽  
Granular Media ◽  
Finite Size ◽  
Spherical Particles ◽  
Annual Review ◽  
Publication Date ◽  
Zero Gravity ◽  
Inertial Particles

This review is motivated by the fast progress in our understanding of the physics of particle-laden turbulence in the last decade, partly due to the tremendous advances of measurement and simulation capabilities. The focus is on spherical particles in homogeneous and canonical wall-bounded flows. The analysis of recent data indicates that conclusions drawn in zero gravity should not be extrapolated outside of this condition, and that the particle response time alone cannot completely define the dynamics of finite-size particles. Several breakthroughs have been reported, mostly separately, on the dynamics and turbulence modifications of small inertial particles in dilute conditions and of large weakly buoyant spheres. Measurements at higher concentrations, simulations fully resolving smaller particles, and theoretical tools accounting for both phases are needed to bridge this gap and allow for the exploration of the fluid dynamics of suspensions, from laminar rheology and granular media to particulate turbulence. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 54 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

scholarly journals Effects of dynamic fragmentation on the impact force exerted on rigid barrier: centrifuge modelling

2019 ◽  
Vol 56 (9) ◽  
pp. 1215-1224 ◽  
Author(s):  
C.W.W. Ng ◽  
C.E. Choi ◽  
D.K.H. Cheung ◽  
Y. Cui
Keyword(s):  
Volume Fraction ◽  
Impact Force ◽  
Inertial Particles ◽  
Size Segregation ◽  
Centrifuge Modelling ◽  
Rigid Barrier ◽  
Flow Energy ◽  
Dynamic Fragmentation ◽  
Large Particles ◽  
The Impact

Bi-dispersity is a prerequisite for grain-size segregation, which transports the largest particles to the flow front. These large and inertial particles can fragment upon impacting a barrier. The amount of fragmentation during impact strongly influences the force exerted on a rigid barrier. Centrifuge modelling was adopted to replicate the stresses for studying the effects of bi-dispersity in a granular assembly and dynamic fragmentation on the impact force exerted on a model rigid barrier. To study the effects of bi-dispersity, the ratio between the diameters of small and large particles (δs/δl), characterizing the particle-size distribution (PSD), was varied as 0.08, 0.26, and 0.56. The volume fraction of the large particles was kept constant. A δs/δl tending towards unity characterizes inertial flow that exerts sharp impulses, and a diminishing δs/δl characterizes the progressive attenuation of these sharp impulses by the small particles. Flows dominated by grain-contact stresses (δs/δl < 0.26), as characterized by the Savage number, are effective at attenuating dispersive stresses of the large particles, which are responsible for reducing dynamic fragmentation. By contrast, flows dominated by grain-inertial stresses (δs/δl > 0.26) exhibit up to 66% more impulses and 4.3 times more fragmentation. Dynamic fragmentation of bi-disperse flows impacting a rigid barrier can dissipate about 30% of the total flow energy.

scholarly journals On the transition between turbulence regimes in particle-laden channel flows

2018 ◽  
Vol 845 ◽  
pp. 499-519 ◽  
Author(s):  
Jesse Capecelatro ◽  
Olivier Desjardins ◽  
Rodney O. Fox
Keyword(s):  
Reynolds Number ◽  
Fluid Phase ◽  
Stokes Number ◽  
Channel Flows ◽  
High Mass ◽  
Inertial Particles ◽  
Mass Loading ◽  
Two Phase ◽  
Phase Dynamics ◽  
Wide Range

Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e.  drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

Influence of Gravity Driven Convection on the Directional Solidification of Bi/MnBi Eutectic Composites

1981 ◽  
Vol 9 ◽  
Author(s):  
Ron G. Pirich ◽  
D.J. Larson
Keyword(s):  
Directional Solidification ◽  
Normal Gravity ◽  
Volume Fraction ◽  
Sounding Rocket ◽  
Low Gravity ◽  
Gravity Driven ◽  
Morphological Differences ◽  
Mnbi Phase ◽  
Irregular Interface

ABSTRACTThe role of gravity on Bridgman-Stockharger directional solidification of eutectic Bi/MnBi has been studied in reduced gravity aboard NASA sounding rocket SPAR flight experiments and contrasted with normal gravity investigations. The directional solidification of eutectic Ri/MnBi results in a low volume fraction, faceted/nonfaceted aligned rod eutectic whose MnRi rod size, interrod spacing, thermal and magnetic properties are sensitive functions of solidification processing conditions. The morphology of the low-gravity samples showed striking differences compared with identically processed,normal gravity samples grown in the same apparatus. The MnBi rod diameter and interrod spacing distributions were significantly smaller, approximately 50%, for the lowgravity samples compared with identically processed one gravity samples. Accompanying the smaller MnBi rod diameters observed in the flight samples, was an increase in permanent magnet properties which reached greater than 97% of the theoretical maximum.Gravitationally induced thermal instabilities in one-gravity which result in irregular interface movement and associated difficulty of the faceted MnBi phase to branch are suggested to explain the morphological differences between one and low gravity solidification.

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

2010 ◽  
Vol 650 ◽  
pp. 5-55 ◽  
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.

Fracture behavior of short-fiber reinforced materials

1992 ◽  
Vol 7 (11) ◽  
pp. 3120-3131 ◽  
Author(s):  
Michael Murat ◽  
Micha Anholt ◽  
H. Daniel Wagner
Keyword(s):  
Fracture Process ◽  
Fracture Behavior ◽  
Volume Fraction ◽  
Fiber Composite ◽  
Finite Size ◽  
Critical Length ◽  
Short Fiber ◽  
Fiber Volume ◽  
Linear Elastic ◽  
Fiber Reinforced Materials

A discrete model of springs with bond-bending forces is proposed to simulate the fracture process in a composite of short stiff fibers in a softer matrix. Both components are assumed to be linear elastic up to failure. We find that the critical fiber length of a single fiber composite increases roughly linearly with the ratio of the fiber elastic modulus to matrix modulus. The finite size of the lattice in the direction perpendicular to the fiber orientation considerably alters the behavior of the critical length for large values of the modulus ratio. The simulations of the fracture process reveal different fracture behavior as a function of the fiber content and length. We calculate the Young's modulus, fracture stress, and the strain at maximum stress as a function of the fiber volume fraction and aspect ratio. The results are compared with the predictions of other theoretical studies and experiments.

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