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Filippo Coletti - One of the best experts on this subject based on the ideXlab platform.
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experimental study of inertial particles clustering and settling in Homogeneous Turbulence
Journal of Fluid Mechanics, 2019Co-Authors: Alec Petersen, Lucia Baker, Filippo ColettiAbstract:We study experimentally the spatial distribution, settling and interaction of sub-Kolmogorov inertial particles with Homogeneous Turbulence. Utilizing a zero-mean-flow air Turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The Turbulence Reynolds number based on the Taylor microscale ranges from particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the Turbulence. The particle–fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.
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experimental study of inertial particles clustering and settling in Homogeneous Turbulence
arXiv: Fluid Dynamics, 2018Co-Authors: Alec Petersen, Lucia Baker, Filippo ColettiAbstract:We study experimentally the spatial distribution, settling, and interaction of sub-Kolmogorov inertial particles with Homogeneous Turbulence. Utilizing a zero-mean-flow air Turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The Turbulence Reynolds number based on the Taylor microscale ranges from $Re_{\lambda}\approx 200$ - $500$, while the particle Stokes number based on the Kolmogorov scale varies between $St_{\eta} = O(1)$ and $O(10)$. Clustering is confirmed to be most intense for $St_{\eta} \approx 1$, but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and sizes that can reach the integral scale of the Turbulence. Remarkably, the settling velocity of $St_{\eta} \approx 1$ particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the Turbulence. The particle-fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.
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coherent clusters of inertial particles in Homogeneous Turbulence
Journal of Fluid Mechanics, 2017Co-Authors: Lucia Baker, Ari Frankel, Ali Mani, Filippo ColettiAbstract:Despite the widely acknowledged significance of Turbulence-driven clustering, a clear topological definition of particle cluster in turbulent dispersed multiphase flows has been lacking. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to distributions of heavy particles in direct numerical simulations of Homogeneous isotropic Turbulence, with and without gravitational acceleration. Clusters show self-similarity already at length scales larger than twice the Kolmogorov length, as indicated by the fractal nature of their surface and by the power-law decay of their size distribution. The size of the identified clusters extends to the integral scale, with average concentrations that depend on the Stokes number but not on the cluster dimension. Compared to non-clustered particles, coherent clusters show a stronger tendency to sample regions of high strain and low vorticity. Moreover, we find that the clusters align themselves with the local vorticity vector. In the presence of gravity, they tend to align themselves vertically and their fall speed is significantly different from the average settling velocity: for moderate fall speeds they experience stronger settling enhancement than non-clustered particles, while for large fall speeds they exhibit weakly reduced settling. The proposed approach for cluster identification leverages the Voronoi diagram method, but is also compatible with other tessellation techniques such as the classic box-counting method.
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settling of heated particles in Homogeneous Turbulence
9th International Symposium on Turbulence and Shear Flow Phenomena TSFP 2015, 2015Co-Authors: Ari Frankel, Hadi Pouransari, Filippo Coletti, Ali ManiAbstract:We study the case of inertial particles heated by thermal radiation while settling by gravity through a turbulent transparent gas. We consider dilute and optically thin regimes in which each particle receives the same heat flux. Numerical simulations of forced Homogeneous Turbulence are performed taking into account the two-way coupling of both momentum and temperature between the dispersed and continuous phases. Particles much smaller than the smallest flow scales are considered and the point-particle approximation is adopted. The particle Stokes number (based on the Kolmogorov time scale) is of order unity, while the nominal settling velocity is up to an order of magnitude larger than the Kolmogorov velocity, marking a critical difference with previous two-way coupled simulations. It is found that non-heated particles enhance Turbulence when their settling velocity is sufficiently high compared to the Kolmogorov velocity. Energy spectra show that the non-heated particle settling impacts both the very small and very large flow scales, while the intermediate scales are weakly affected. When heated, particles shed plumes of buoyant gas, further modifying the Turbulence structure. At the considered radiation intensities, clustering is strong but the classic mechanism of preferential concentration is modified, while preferential sweeping is eliminated or even reversed. Particle heating also causes a significant reduction of the mean settling velocity, which is caused by rising buoyant plumes in the vicinity of particle clusters. The turbulent kinetic energy is affected non-monotonically as the radiation intensity is increased due to the competing effects of the downward gravitational force and the upward buoyancy force. The thermal radiation influences all scales of the Turbulence. The effects of settling and buoyancy on the Turbulence anisotropy are also discussed.
P A Davidson - One of the best experts on this subject based on the ideXlab platform.
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freely decaying Homogeneous Turbulence generated by multi scale grids
arXiv: Fluid Dynamics, 2011Co-Authors: Per-Åge Krogstad, P A DavidsonAbstract:We investigate wind tunnel Turbulence generated by both conventional and multi-scale grids. Measurements were made in a tunnel which has a large test-section, so that possible side wall effects are very small and the length assures that the Turbulence has time to settle down to a Homogeneous shear-free state. The conventional and multi-scale grids were all designed to produce Turbulence with the same integral scale, so that a direct comparison could be made between the different flows. Our primary finding is that the behavior of the Turbulence behind our multi-scale grids is virtually identical to that behind the equivalent conventional grid. In particular, all flows exhibit a power-law decay of energy, $u^2 \sim t^{-n}$, where $n$ is very close to the classical Saffman exponent of $n = 6/5$. Moreover, all spectra exhibit classical Kolmogorov scaling, with the spectra collapsing on the integral scales at small $k$, and on the Kolmogorov micro-scales at large $k$. Our results are at odds with some other experiments performed on similar multi-scale grids, where significantly higher energy decay exponents and Turbulence levels have been reported.
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the role of angular momentum conservation in Homogeneous Turbulence
Journal of Fluid Mechanics, 2009Co-Authors: P A DavidsonAbstract:Loitsyanky's integral I = − ∫ r 2 〈 u ⋅ u ′〉d r is known to be approximately conserved in certain types of fully developed, isotropic Turbulence, and its near conservation controls the rate of decay of kinetic energy. Landau suggested that this integral is related to the angular momentum H = ∫ ( x × u )d V of some large volume V of the Turbulence, according to the expression I = 〈 H 2 〉/ V . He also suggested that the approximate conservation of I is related to the principle of conservation of angular momentum. However, Landau's analysis can be criticized because, formally, it applies only to inHomogeneous Turbulence evolving in a closed domain. So how are we to interpret the near conservation of I ? And what is its relationship, if any, to angular momentum conservation? We show that the key to extending Landau's analysis to strictly Homogeneous Turbulence is to rewrite Loitsyansky's integral in terms of the vector potential of the velocity field, i.e. I = 6 ∫〈 A ⋅ A ′〉d r , where ∇ × A = u . This yields I = 6〈[∫ V A d V ] 2 〉/ V for any large spherical volume V of radius R . Crucially, J = 3∫ V A d V can be rewritten as the weighted integral of the angular momentum density throughout all space. This fundamentally changes the way in which we interpret the dynamical behaviour of I . For example, we show that the conservation of 〈 J 2 〉/ V , and hence of I , which occurs when the long-range correlations are weak, is a direct consequence of the decorrelation of the flux of angular momentum out through a spherical control surface S and the local angular momentum in the vicinity of S . Thus, within the framework of strictly Homogeneous Turbulence, we provide the first self-consistent interpretation of Loitsyanky's integral in terms of angular momentum conservation. We also show that essentially the same ideas carry over to certain types of anisotropic Turbulence, such as magnetohydrodynamic (MHD), rotating and stratified Turbulence. This is important because conservation of angular momentum, which manifests itself in the form of a Loitsyansky-like invariant, places a fundamental restriction on the way in which the integral scales can evolve in such Turbulence. This, in turn, controls the rate of decay of energy. We illustrate this by deriving new decay laws for MHD and stratified Turbulence. The MHD decay laws are consistent with the available numerical evidence, but further study is required to verify, or otherwise, the predictions for stratified Turbulence.
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structure formation in Homogeneous freely decaying rotating Turbulence
Journal of Fluid Mechanics, 2008Co-Authors: P J Staplehurst, P A Davidson, Stuart B DalzielAbstract:One of the most striking features of rotating Turbulence is the inevitable appearance of large-scale columnar structures. Whilst these structures are frequently observed, the processes by which they are created are still poorly understood. In this paper we consider the emergence of these structures from freely decaying, rotating Turbulence with Ro ∼ 1. Our study follows the conjecture by Davidson, Staplehurst & Dalziel ( J. Fluid Mech. , vol. 557, 2006, p. 135) that the structure formation may be due to linear inertial wave propagation, which was shown to be consistent with the growth of columnar eddies in inHomogeneous Turbulence. Here we extend that work and consider the case of Homogeneous Turbulence. We describe laboratory experiments where Homogeneous Turbulence is created in a rotating tank. The Turbulence is generated with Ro ∼ 1, and as the energy decays, the formation of columnar vortices is observed. The axial growth of these columnar structures is then measured using two-point correlations and in all cases the results are consistent with structure formation via linear inertial wave propagation. In particular, we obtain a self-similar collapse of the two-point correlations when the axial coordinate is normalized by Ω tb , where b is a measure of the integral scale in the horizontal plane and Ω is the rotation rate. Although our results do not exclude the possibility of significant nonlinear dynamics, they are consistent with the conjecture of Davidson et al . (2006) that linear dynamics play a strong guiding hand in structure formation.
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linear and angular momentum invariants in Homogeneous Turbulence
2008Co-Authors: P A Davidson, Takaki Ishida, Yukio KanedaAbstract:We discuss the constraints imposed on the evolution of freely-decaying Turbulence by the laws of conservation of linear and angular momentum. In particular, we explain the results of recent numerical simulations in terms of angular momentum conservation. These simulations show that, once the Turbulence reaches a mature state, with a fully-developed vorticity field, its kinetic energy decays as t-10/7, a result which is consistent with the classical theories of Landau and Kolmogorov, and inconsistent with Markovianised closure models.
Toshiyuki Gotoh - One of the best experts on this subject based on the ideXlab platform.
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statistics of a passive scalar in Homogeneous Turbulence
New Journal of Physics, 2004Co-Authors: Takeshi Watanabe, Toshiyuki GotohAbstract:Statistics of a passive scalar with Sc=1 transported by steady Homogeneous Turbulence at Rλ=427 and Pλ=427 is studied by using high-resolution direct numerical simulation. The Obukhov–Corrsin constant of the three-dimensional scalar spectrum in the inertial-convective range is found to be 0.68±0.04. It is proved that the -law for the scalar-velocity triple correlation holds in both inertial-convective and viscous-convective ranges when Sc>1, and found that the -law is approached with increase in Peclet number. Structure functions of the passive scalar increment and their local scaling exponents are computed as functions of the separation distance, and it is found that there exist two scaling ranges: the inertial-convective range and a narrow precursory range to the viscous-convective range. The scaling exponents in the inertial-convective range are found to be smaller than those of the velocity field and do not saturate, whereas they saturate at about 1.5 in the short precursory range to the viscous-convective range. It is also found that, contrary to the scalar case, the mixed scalar velocity structure function has a well-developed single scaling range. The scalar and scalar dissipation fields are visualized and compared with the kinetic energy dissipation field. The scalar field has a particular shape with a large-scale plateau, sharp cliff and deep valley, a mesa-canyon structure.
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pressure spectrum in Homogeneous Turbulence
Physical Review Letters, 2001Co-Authors: Toshiyuki Gotoh, Daigen FukayamaAbstract:The pressure spectrum in Homogeneous steady Turbulence is studied using direct numerical simulation with resolution up to ${1024}^{3}$ and the Reynolds number ${R}_{\ensuremath{\lambda}}$ between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant $K\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.65\ifmmode\pm\else\textpm\fi{}0.05$ followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately $P(k){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}B}_{p}{\overline{\ensuremath{\epsilon}}}^{4/3}{k}^{\ensuremath{-}7/3}$ with ${B}_{p}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8.0\ifmmode\pm\else\textpm\fi{}0.5$, and followed by a bump of nearly ${k}^{\ensuremath{-}5/3}$ at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.
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pressure spectrum in Homogeneous Turbulence
Physical Review Letters, 2001Co-Authors: Toshiyuki Gotoh, Daigen FukayamaAbstract:The pressure spectrum in Homogeneous steady Turbulence is studied using direct numerical simulation with resolution up to 1024(3) and the Reynolds number R(lambda) between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant K = 1.65+/-0.05 followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately P(k) = B(p)epsilon;(4/3)k(-7/3) with B(p) = 8.0+/-0.5, and followed by a bump of nearly k(-5/3) at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.
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Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence
Journal of the Physical Society of Japan, 1999Co-Authors: Naoya Takahashi, Tohru Nakano, Toshiyuki Gotoh, Tsutomu Kambe, Kiyoshi YamamotoAbstract:Two conditional averages for the longitudinal velocity increment u_r of the simulated Turbulence are calculated: h(u_r) is the average of the increment of the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the corresponding one of the square of the difference of the gradient of the velocity field. Based on the physical argument, we suggest the formulae for h and g, which are quite satisfactorily fitted to the 512^3 DNS data. The predicted PDF is characterized as (1) the Gaussian distribution for the small amplitudes, (2) the exponential distribution for the large ones, and (3) a prefactor before the exponential function for the intermediate ones.
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probability density function of longitudinal velocity increment in Homogeneous Turbulence
Journal of the Physical Society of Japan, 1999Co-Authors: Naoya Takahashi, Tohru Nakano, Toshiyuki Gotoh, Tsutomu Kambe, Kiyoshi YamamotoAbstract:Two conditional averages for the longitudinal velocity increment u r are considered: h ( u r ) is the average of the difference of the Laplacian of the velocity field with the u r value fixed, while g ( u r ) is the corresponding one of the square of the difference of the velocity gradient. The fitting formulae for h and g are derived for the 512 3 data of the direct numerical simulation. The computed PDF is characterized as (1) the Gaussian distribution for smaller amplitudes, (2) the exponential distribution for larger ones, and (3) the stretched exponential distribution for intermediate ones due to a factor in front of the exponential function.
Martin R Maxey - One of the best experts on this subject based on the ideXlab platform.
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modulation of Homogeneous Turbulence seeded with finite size bubbles or particles
International Journal of Multiphase Flow, 2010Co-Authors: Kyongmin Yeo, Suchuan Dong, Eric Climent, Martin R MaxeyAbstract:The dynamics of Homogeneous, isotropic Turbulence seeded with finite sized particles or bubbles is investigated in a series of numerical simulations, using the force-coupling method for the particle phase and low wavenumber forcing of the flow to sustain the Turbulence. Results are given on the modulation of the Turbulence due to massless bubbles, neutrally buoyant particles and inertial particles of specific density 1.4 at volumetric concentrations of 6%. Buoyancy forces due to gravity are excluded to emphasize finite size and inertial effects for the bubbles or particles and their interactions with the Turbulence. Besides observing the classical entrapment of bubbles and the expulsion of inertial particles by vortex structures, we analyze the Lagrangian statistics for the velocity and acceleration of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the smallscale kinetic energy is significantly enhanced. Unexpectedly, the modulation of Turbulence depends only slightly on the dispersion characteristics (bubble entrapment in vortices or inertial sweeping of the solid particles) but is closely related to the stresslet component (finite size effect) of the flow disturbances. The pivoting wavenumber characterizing the transition from damped to enhanced energy content is shown to vary with the size of the bubbles or particles. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.
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settling velocity and concentration distribution of heavy particles in Homogeneous isotropic Turbulence
Journal of Fluid Mechanics, 1993Co-Authors: Lianping Wang, Martin R MaxeyAbstract:The average settling velocity in Homogeneous Turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic Homogeneous Turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the Turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.
G C Truesdell - One of the best experts on this subject based on the ideXlab platform.
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on the two way interaction between Homogeneous Turbulence and dispersed solid particles ii particle dispersion
Physics of Fluids, 1994Co-Authors: G C Truesdell, S ElghobashiAbstract:Part I of this paper [Elghobashi and Truesdell, Phys. Fluids A 5, 1790 (1993)] examined the modulation of Turbulence by the particles. Here the effects of the two‐way interaction on particle dispersion are discussed. In zero gravity, the two‐way coupling enhances the alignment of the surrounding fluid velocity vector with the direction of the solid particle trajectory. This alignment reduces the mean‐square relative velocity and increases the Lagrangian velocity autocorrelation coefficient of the solid particle, the fluid point and the surrounding fluid, and the mean‐square displacement of the solid particles. However, the fluid point mean‐square displacement decreases because the larger inertia of the solid particles increases the decay rate of Turbulence energy. In gravity environment, the particles augment the component of Turbulence energy in the gravity direction, and thus increase the mean‐square displacement of the solid particles and fluid points in that direction. However, their dispersion in the lateral directions is reduced due to the crossing trajectories effect [Yudine, Adv. Geophys. 6, 185 (1959)].
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on the two way interaction between Homogeneous Turbulence and dispersed solid particles i Turbulence modification
Physics of Fluids, 1993Co-Authors: S Elghobashi, G C TruesdellAbstract:The modification of decaying Homogeneous Turbulence due to its interaction with dispersed small solid particles (d/η<1), at a volumetric loading ratio φv≤5×10−4, is studied using direct numerical simulation. The results show that the particles increase the fluid Turbulence energy at high wave numbers. This increase of energy is accompanied by an increase of the viscous dissipation rate, and, hence, an increase in the rate of energy transfer T(k) from the large‐scale motion. Thus, depending on the conditions at particle injection, the fluid Turbulence kinetic energy may increase initially. But, in the absence of external sources (shear or buoyancy), the Turbulence energy eventually decays faster than in the particle‐free Turbulence. In gravitational environment, particles transfer their momentum to the small‐scale motion but in an anisotropic manner. The pressure‐strain correlation acts to remove this anisotropy by transferring energy from the direction of gravity to the other two directions, but at the sa...