1
|
Matsuda K, Yoshimatsu K, Schneider K. Heavy Particle Clustering in Inertial Subrange of High-Reynolds Number Turbulence. PHYSICAL REVIEW LETTERS 2024; 132:234001. [PMID: 38905672 DOI: 10.1103/physrevlett.132.234001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2024] [Accepted: 05/06/2024] [Indexed: 06/23/2024]
Abstract
Direct numerical simulation of homogeneous isotropic turbulence shows pronounced clustering of inertial particles in the inertial subrange at high Reynolds number, in addition to the clustering typically observed in the near dissipation range. The clustering in the inertial subrange is characterized by the bump in the particle number density spectra and is due to modulation of preferential concentration. The number density spectrum can be modeled by a rational function of the scale-dependent Stokes number.
Collapse
|
2
|
Maity P. Heavy inertial particles in rotating turbulence: Distribution of particles in flow and evolution of Lagrangian trajectories. Phys Rev E 2023; 107:065107. [PMID: 37464649 DOI: 10.1103/physreve.107.065107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 05/26/2023] [Indexed: 07/20/2023]
Abstract
We revisit the problem of heavy particles suspended in homogeneous box turbulence flow subjected to rotation along the vertical axis, which introduces anisotropy along the vertical and horizontal planes. We investigate the effects of the emergent structures due to rotation, on the spatial distribution and temporal statistics of the particles. The distribution of particles in the flow are studied using the joint probability distribution function (JPDFs) of the second and third principle invariants of the velocity gradient tensor, Q and R. At high rotation rates, the JPDFs of Lagrangian Q-R plots show remarkable deviations from the well-known teardrop shape. The cumulative probability distribution functions for times during which a particle remains in vortical or straining regions show exponentially decaying tails except for the deviations at the highest rotation rate. The average residence times of the particles in vortical and straining regions are also affected considerably due to the addition of rotation. Furthermore, we compute the temporal velocity autocorrelation and connect it to the Lagrangian anisotropy in presence of rotation. The spatial and temporal statistics of the particles are determined by a complex competition between the rotation rate and inertia of the particle.
Collapse
Affiliation(s)
- Priyanka Maity
- Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany
| |
Collapse
|
3
|
Lee S, Lee C. Identification of a particle collision as a finite-time blowup in turbulence. Sci Rep 2023; 13:181. [PMID: 36604443 PMCID: PMC9814516 DOI: 10.1038/s41598-022-27305-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 12/29/2022] [Indexed: 01/06/2023] Open
Abstract
We propose an Eulerian approach to investigate the motion of particles in turbulence under the assumption that the motion of particles remains smooth in space and time until a collision between particles occurs. When the first collision happens, particle velocity loses [Formula: see text] continuity, resulting in a finite-time blowup. The corresponding singularities in particle velocity gradient, particle number density, and particle vorticity for various Stokes numbers and gravity factors are numerically investigated for the first time in a simple two-dimensional Taylor-Green vortex flow, two-dimensional decaying turbulence, and three-dimensional isotropic turbulence. In addition to the critical Stokes number above which a collision begins to occur, the flow condition leading to collision is revealed; particles tend to collide in very thin shear layer constructed by two parallel same-signed vortical structures when Stokes number is above the critical one.
Collapse
Affiliation(s)
- Seulgi Lee
- grid.15444.300000 0004 0470 5454Department of Mechanical Engineering, Yonsei University, Seoul, 03722 South Korea
| | - Changhoon Lee
- grid.15444.300000 0004 0470 5454Department of Mechanical Engineering & School of Mathematics and Computing, Yonsei University, Seoul, 03722 South Korea
| |
Collapse
|
4
|
Gupta M, Chaudhuri P, Bec J, Ray SS. Turbulent route to two-dimensional soft crystals. Phys Rev E 2022; 106:L062601. [PMID: 36671119 DOI: 10.1103/physreve.106.l062601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Accepted: 11/09/2022] [Indexed: 06/17/2023]
Abstract
We investigate the effect of a two-dimensional, incompressible, turbulent flow on soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag and short-range interparticle interactions. We quantify this phase through the bond order parameter and local density fluctuations and find a sharp transition between the crystalline and noncrystalline phases as a function of the Stokes number. Furthermore, the nature of preferential concentration, characterized by the correlation dimension, is significantly different from that of particle-laden flows in the absence of repulsive potentials.
Collapse
Affiliation(s)
- Mohit Gupta
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
| | - Jérémie Bec
- Université Côte d'Azur, Inria, CNRS, Cemef, 06902 Sophia-Antipolis, France
- MINES ParisTech, PSL Research University, CNRS, CEMEF, 06904 Sophia-Antipolis, France
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| |
Collapse
|
5
|
Abstract
Due to the significant reduction in water droplet size caused by the strong air-water interaction in the spray nozzle, air-mist spray is one of the promising technologies for achieving high-rate heat transfer. This study numerically analyzed air-mist spray produced by a flat-fan atomizer using three-dimensional computational fluid dynamics simulations, and a multivariable linear regression was used to develop a correlation to predict the heat transfer coefficient using the casting operating conditions such as air-pressure, water flow rate, casting speed, and standoff distance. A four-step simulation approach was used to simulate the air-mist spray cooling capturing the turbulence and mixing of the two fluids in the nozzle, droplet formation, droplet transport and impingement heat transfer. Validations were made on the droplet size and on the VOF-DPM model which were in good agreement with experimental results. A 33% increase in air pressure increases the lumped HTC by 3.09 ± 2.07% depending on the other casting parameters while an 85% increase in water flow rate reduces the lumped HTC by 4.61 ± 2.57%. For casting speed, a 6.5% decrease in casting speed results in a 1.78 ± 1.42% increase in the lumped HTC. The results from this study would provide useful information in the continuous casting operations and optimization.
Collapse
|
6
|
Falkinhoff F, Obligado M, Bourgoin M, Mininni PD. Preferential Concentration of Free-Falling Heavy Particles in Turbulence. PHYSICAL REVIEW LETTERS 2020; 125:064504. [PMID: 32845665 DOI: 10.1103/physrevlett.125.064504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Revised: 04/16/2020] [Accepted: 07/20/2020] [Indexed: 06/11/2023]
Abstract
We present a sweep-stick mechanism for heavy particles transported by a turbulent flow under the action of gravity. Direct numerical simulations show that these particles preferentially explore regions of the flow with close to zero Lagrangian acceleration. However, the actual Lagrangian acceleration of the fluid elements where particles accumulate is not zero, and has a dependence on the Stokes number, the gravity acceleration, and the settling velocity of the particles.
Collapse
Affiliation(s)
- F Falkinhoff
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, & IFIBA, CONICET, Ciudad Universitaria, Buenos Aires 1428, Argentina
- Université Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, 46 all ée dItalie, F-69342 Lyon, France
| | - M Obligado
- Université Grenoble Alpes, CNRS, Grenoble-INP, LEGI, F-38000 Grenoble, France
| | - M Bourgoin
- Université Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, 46 all ée dItalie, F-69342 Lyon, France
| | - P D Mininni
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, & IFIBA, CONICET, Ciudad Universitaria, Buenos Aires 1428, Argentina
| |
Collapse
|
7
|
Anand P, Ray SS, Subramanian G. Orientation Dynamics of Sedimenting Anisotropic Particles in Turbulence. PHYSICAL REVIEW LETTERS 2020; 125:034501. [PMID: 32745414 DOI: 10.1103/physrevlett.125.034501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Revised: 05/12/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneous isotropic turbulence using direct numerical simulations and theory. The gravity-induced inertial torque acting on sub-Kolmogorov spheroids leads to pronouncedly non-Gaussian orientation distributions localized about the broadside-on (to gravity) orientation. Orientation distributions and average settling velocities are obtained over a wide range of spheroid aspect ratios, Stokes, and Froude numbers. Orientational moments from the simulations compare well with analytical predictions in the inertialess rapid-settling limit, with both exhibiting a nonmonotonic dependence on spheroid aspect ratio. Deviations arise at Stokes numbers of order unity due to a spatially inhomogeneous particle concentration field resulting from a preferential sweeping effect; as a consequence, the time-averaged particle settling velocities exceed the orientationally averaged estimates.
Collapse
Affiliation(s)
- Prateek Anand
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Ganesh Subramanian
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| |
Collapse
|
8
|
Singh R, Gupta M, Picardo JR, Vincenzi D, Ray SS. Elastoinertial chains in a two-dimensional turbulent flow. Phys Rev E 2020; 101:053105. [PMID: 32575226 DOI: 10.1103/physreve.101.053105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 02/28/2020] [Indexed: 12/13/2022]
Abstract
The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modeled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions among inertial beads result in a nontrivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, noninteracting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.244501]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.
Collapse
Affiliation(s)
- Rahul Singh
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Mohit Gupta
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.,School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Jason R Picardo
- Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
| | | | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| |
Collapse
|
9
|
Bhatnagar A. Statistics of relative velocity for particles settling under gravity in a turbulent flow. Phys Rev E 2020; 101:033102. [PMID: 32289925 DOI: 10.1103/physreve.101.033102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Accepted: 02/07/2020] [Indexed: 06/11/2023]
Abstract
We study the joint probability distributions of separation R and radial component of the relative velocity V_{R} of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitative nature of the joint distributions remains the same as no-gravity case. Distributions of V_{R} for fixed values of R show a power-law dependence on V_{R} for a range of V_{R}; the exponent of the power law depends on the gravity. Effects of gravity are also manifested in the following ways: (a) Moments of the distributions are anisotropic; degree of anisotropy depends on particle's Stokes number, but does not depend on R for small values of R. (b) Mean velocity of collision between two particles is decreased for particles having equal Stokes numbers but increased for particles having different Stokes numbers. For the later, collision velocity is set by the difference in their settling velocities.
Collapse
Affiliation(s)
- Akshay Bhatnagar
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| |
Collapse
|
10
|
Dey S, Zeeshan Ali S, Padhi E. Terminal fall velocity: the legacy of Stokes from the perspective of fluvial hydraulics. Proc Math Phys Eng Sci 2019; 475:20190277. [PMID: 31534429 DOI: 10.1098/rspa.2019.0277] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Accepted: 08/02/2019] [Indexed: 11/12/2022] Open
Abstract
This review article, dedicated to the bicentenary celebration of Sir George Gabriel Stokes' birthday, presents the state-of-the-science of terminal fall velocity, highlighting his rich legacy from the perspective of fluvial hydraulics. It summarizes the fluid drag on a particle and the current status of the drag coefficient from both the theoretical and empirical formulations, highlighting the three major realms-Stokesian, transitional and Newtonian realms. The force system that drives the particle motion falling through a fluid is described. The response of terminal fall velocity to key factors, which include particle shape, hindered settling and turbulence (nonlinear drag, vortex trapping, fast tracking and effects of loitering), is delineated. The article puts into focus the impact of terminal fall velocity on fluvial hydraulics, discussing the salient role that the terminal fall velocity plays in governing the hydrodynamics of the sediment threshold, bedload transport and suspended load transport. Finally, an innovative perspective is presented on the subject's future research track, emphasizing open questions.
Collapse
Affiliation(s)
- Subhasish Dey
- Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India.,Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal 700108, India.,Department of Hydraulic Engineering, State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing 100084, People's Republic of China
| | - Sk Zeeshan Ali
- Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
| | - Ellora Padhi
- Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
| |
Collapse
|
11
|
Agasthya L, Picardo JR, Ravichandran S, Govindarajan R, Ray SS. Understanding droplet collisions through a model flow: Insights from a Burgers vortex. Phys Rev E 2019; 99:063107. [PMID: 31330678 DOI: 10.1103/physreve.99.063107] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2018] [Indexed: 11/06/2022]
Abstract
We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of polydisperse suspensions in this enhancement. Our work uncovers an important principle, which, if valid for realistic turbulent flows, may be a factor in how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.
Collapse
Affiliation(s)
- Lokahith Agasthya
- Indian Institute for Science Education and Research, Pune, 411008, India.,International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India.,Department of Physics and INFN, University of Rome Tor Vergata,Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Jason R Picardo
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - S Ravichandran
- Nordita, KTH Royal Institute of Technology and Stockholm University, 10691 Stockholm, Sweden
| | - Rama Govindarajan
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| |
Collapse
|
12
|
Picardo JR, Vincenzi D, Pal N, Ray SS. Preferential Sampling of Elastic Chains in Turbulent Flows. PHYSICAL REVIEW LETTERS 2018; 121:244501. [PMID: 30608752 DOI: 10.1103/physrevlett.121.244501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2018] [Indexed: 06/09/2023]
Abstract
A string of tracers interacting elastically in a turbulent flow is shown to have a dramatically different behavior when compared to the noninteracting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: An elastic chain is trapped in the vortical regions. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain via the number of links that form it is also examined.
Collapse
Affiliation(s)
- Jason R Picardo
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | | | - Nairita Pal
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| |
Collapse
|
13
|
Larsen ML, Shaw RA, Kostinski AB, Glienke S. Fine-Scale Droplet Clustering in Atmospheric Clouds: 3D Radial Distribution Function from Airborne Digital Holography. PHYSICAL REVIEW LETTERS 2018; 121:204501. [PMID: 30500255 DOI: 10.1103/physrevlett.121.204501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Indexed: 06/09/2023]
Abstract
The extent of droplet clustering in turbulent clouds has remained largely unquantified, and yet is of possible relevance to precipitation formation and radiative transfer. To that end, data gathered by an airborne holographic instrument are used to explore the three-dimensional spatial statistics of cloud droplet positions in homogeneous stratiform boundary-layer clouds. The three-dimensional radial distribution functions g(r) reveal unambiguous evidence of droplet clustering. Three key theoretical predictions are observed: the existence of positive correlations, onset of correlation in the turbulence dissipation range, and monotonic increase of g(r) with decreasing r. This implies that current theory captures the essential processes contributing to clustering, even at large Reynolds numbers typical of the atmosphere.
Collapse
Affiliation(s)
- Michael L Larsen
- Department of Physics and Astronomy, College of Charleston, Charleston, South Carolina 29424, USA
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
| | - Raymond A Shaw
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
| | - Alexander B Kostinski
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
| | - Susanne Glienke
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
- Johannes Gutenberg University, Mainz, 55099, Germany
- Max Planck Institute for Chemistry, Mainz, 55128, Germany
| |
Collapse
|
14
|
Roy A, Gupta A, Ray SS. Inertial spheroids in homogeneous, isotropic turbulence. Phys Rev E 2018; 98:021101. [PMID: 30253548 DOI: 10.1103/physreve.98.021101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2018] [Indexed: 11/07/2022]
Abstract
We study the rotational dynamics of inertial disks and rods in three-dimensional, homogeneous, isotropic turbulence. In particular, we show how the alignment and the decorrelation timescales of such spheroids depend, critically, on both the level of inertia and the aspect ratio of these particles. These results illustrate the effect of inertia-which leads to a preferential sampling of the local flow geometry-on the statistics of both disks and rods in a turbulent flow. Our results are important for a variety of natural and industrial settings where the turbulent transport of asymmetric, spheroidal inertial particles is ubiquitous.
Collapse
Affiliation(s)
- Amal Roy
- Department of Mathematics, Indian Institute of Science, Bangalore 560012, India.,International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| | - Anupam Gupta
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
| |
Collapse
|
15
|
Gustavsson K, Jucha J, Naso A, Lévêque E, Pumir A, Mehlig B. Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence. PHYSICAL REVIEW LETTERS 2017; 119:254501. [PMID: 29303314 DOI: 10.1103/physrevlett.119.254501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2017] [Indexed: 06/07/2023]
Abstract
The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.
Collapse
Affiliation(s)
- K Gustavsson
- Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden
| | - J Jucha
- Laboratoire de Physique, Ecole Normale Supérieure de Lyon and CNRS, F-69007 Lyon, France
- Projektträger Jülich, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
| | - A Naso
- LMFA, Ecole Centrale de Lyon and CNRS, F-69134 Ecully, France
| | - E Lévêque
- LMFA, Ecole Centrale de Lyon and CNRS, F-69134 Ecully, France
| | - A Pumir
- Laboratoire de Physique, Ecole Normale Supérieure de Lyon and CNRS, F-69007 Lyon, France
| | - B Mehlig
- Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden
| |
Collapse
|
16
|
Meibohm J, Pistone L, Gustavsson K, Mehlig B. Relative velocities in bidisperse turbulent suspensions. Phys Rev E 2017; 96:061102. [PMID: 29347374 DOI: 10.1103/physreve.96.061102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2017] [Indexed: 06/07/2023]
Abstract
We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analyzing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, St, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal St. The power-law exponent is a nonanalytic function of the mean Stokes number St[over ¯], so that the exponent cannot be calculated in perturbation theory around the advective limit. When the Stokes-number difference is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if St[over ¯] is large enough.
Collapse
Affiliation(s)
- J Meibohm
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| | - L Pistone
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| | - K Gustavsson
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| | - B Mehlig
- Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
| |
Collapse
|
17
|
Enhanced droplet collision rates and impact velocities in turbulent flows: The effect of poly-dispersity and transient phases. Sci Rep 2017; 7:12231. [PMID: 28947811 PMCID: PMC5613015 DOI: 10.1038/s41598-017-12093-0] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Accepted: 09/04/2017] [Indexed: 11/09/2022] Open
Abstract
We compare the collision rates and the typical collisional velocities amongst droplets of different sizes in a poly-disperse suspension advected by two- and three-dimensional turbulent flows. We show that the collision rate is enhanced in the transient phase for droplets for which the size-ratios between the colliding pairs is large as well as obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. Our results suggest that an explanation of the rapid growth of droplets, e.g., in warm clouds, may well lie in the dynamics of particles in transient phases where increased collision rates between large and small particles could result in runaway process. Our results are also important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining precise coalescence kernels in such systems.
Collapse
|
18
|
Chen J, Jin G. Large-eddy simulation of turbulent preferential concentration and collision of bidisperse heavy particles in isotropic turbulence. POWDER TECHNOL 2017. [DOI: 10.1016/j.powtec.2016.12.069] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
19
|
Bhatnagar A, Gupta A, Mitra D, Pandit R, Perlekar P. How long do particles spend in vortical regions in turbulent flows? Phys Rev E 2016; 94:053119. [PMID: 27967067 DOI: 10.1103/physreve.94.053119] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2016] [Indexed: 11/07/2022]
Abstract
We obtain the probability distribution functions (PDFs) of the time that a Lagrangian tracer or a heavy inertial particle spends in vortical or strain-dominated regions of a turbulent flow, by carrying out direct numerical simulations of such particles advected by statistically steady, homogeneous, and isotropic turbulence in the forced, three-dimensional, incompressible Navier-Stokes equation. We use the two invariants, Q and R, of the velocity-gradient tensor to distinguish between vortical and strain-dominated regions of the flow and partition the Q-R plane into four different regions depending on the topology of the flow; out of these four regions two correspond to vorticity-dominated regions of the flow and two correspond to strain-dominated ones. We obtain Q and R along the trajectories of tracers and heavy inertial particles and find out the time t_{pers} for which they remain in one of the four regions of the Q-R plane. We find that the PDFs of t_{pers} display exponentially decaying tails for all four regions for tracers and heavy inertial particles. From these PDFs we extract characteristic time scales, which help us to quantify the time that such particles spend in vortical or strain-dominated regions of the flow.
Collapse
Affiliation(s)
- Akshay Bhatnagar
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.,Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| | - Anupam Gupta
- Laboratoire de Génie Chimique, Universite de Toulouse, INPT-UPS, 31030 Toulouse, France
| | - Dhrubaditya Mitra
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Prasad Perlekar
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| |
Collapse
|
20
|
Nicolleau FCGA, Farhan M, Nowakowski AF. Effect of the energy-spectrum law on clustering patterns for inertial particles subjected to gravity in kinematic simulation. Phys Rev E 2016; 94:043109. [PMID: 27841627 DOI: 10.1103/physreve.94.043109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2016] [Indexed: 06/06/2023]
Abstract
We study the clustering of inertial particles using a periodic kinematic simulation. Particle clustering is observed for different pairs of Stokes number and Froude number and different spectral power laws (1.4≤p≤2.1). The main focus is to identify and then quantify the effect of p on the clustering attractor-by attractor we mean the set of points in the physical space where the particles settle when time tends to infinity. It is observed that spectral power laws can have a dramatic effect on the attractor shape. In particular, we observed an attractor type which was not present in previous studies for Kolmogorov spectra (p=5/3).
Collapse
Affiliation(s)
- F C G A Nicolleau
- Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom and Sorbonne Universités, Université Pierre et Marie Curie, Paris 6 and Institut Jean le Rond dAlembert, CNRS UMR 7190, Paris, France
| | - M Farhan
- Department of Mechanical Engineering of the University of Engineering and Technology Lahore, Pakistan and Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom
| | - A F Nowakowski
- Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom
| |
Collapse
|
21
|
Mathai V, Calzavarini E, Brons J, Sun C, Lohse D. Microbubbles and Microparticles are Not Faithful Tracers of Turbulent Acceleration. PHYSICAL REVIEW LETTERS 2016; 117:024501. [PMID: 27447509 DOI: 10.1103/physrevlett.117.024501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2016] [Indexed: 06/06/2023]
Abstract
We report on the Lagrangian statistics of acceleration of small (sub-Kolmogorov) bubbles and tracer particles with Stokes number St≪1 in turbulent flow. At a decreasing Reynolds number, the bubble accelerations show deviations from that of tracer particles; i.e., they deviate from the Heisenberg-Yaglom prediction and show a quicker decorrelation despite their small size and minute St. Using direct numerical simulations, we show that these effects arise due the drift of these particles through the turbulent flow. We theoretically predict this gravity-driven effect for developed isotropic turbulence, with the ratio of Stokes to Froude number or equivalently the particle drift velocity governing the enhancement of acceleration variance and the reductions in correlation time and intermittency. Our predictions are in good agreement with experimental and numerical results. The present findings are relevant to a range of scenarios encompassing tiny bubbles and droplets that drift through the turbulent oceans and the atmosphere. They also question the common usage of microbubbles and microdroplets as tracers in turbulence research.
Collapse
Affiliation(s)
- Varghese Mathai
- Physics of Fluids Group, Faculty of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Enrico Calzavarini
- Université de Lille, CNRS, FRE 3723, LML, Laboratoire de Mécanique de Lille, F 59000 Lille, France
| | - Jon Brons
- Physics of Fluids Group, Faculty of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Applied Mathematics Research Centre, Faculty of Engineering and Computing, Coventry University, Priory Street, Coventry CV1 5FB, United Kingdom
| | - Chao Sun
- Physics of Fluids Group, Faculty of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Center for Combustion Energy and Department of Thermal Engineering, Tsinghua University, 100084 Beijing, China
| | - Detlef Lohse
- Physics of Fluids Group, Faculty of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| |
Collapse
|
22
|
Sardina G, Picano F, Brandt L, Caballero R. Continuous Growth of Droplet Size Variance due to Condensation in Turbulent Clouds. PHYSICAL REVIEW LETTERS 2015; 115:184501. [PMID: 26565469 DOI: 10.1103/physrevlett.115.184501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2014] [Indexed: 05/26/2023]
Abstract
We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate proportional to the large-to-small turbulent scale separation and to the turbulence integral scales but independent of the mean turbulent dissipation. Direct numerical simulations confirm this result and produce realistically broad droplet size spectra over time intervals of 20 min, comparable with the time of rain formation.
Collapse
Affiliation(s)
- Gaetano Sardina
- Department of Meteorology and SeRC, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Francesco Picano
- Linné FLOW Centre and SeRC, KTH Mechanics, SE-100 44 Stockholm, Sweden
- Department of Industrial Engineering, University of Padova, 35131 Padova, Italy
| | - Luca Brandt
- Linné FLOW Centre and SeRC, KTH Mechanics, SE-100 44 Stockholm, Sweden
| | - Rodrigo Caballero
- Department of Meteorology and SeRC, Stockholm University, SE-106 91 Stockholm, Sweden
| |
Collapse
|
23
|
Perrin VE, Jonker HJJ. Relative velocity distribution of inertial particles in turbulence: A numerical study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:043022. [PMID: 26565347 DOI: 10.1103/physreve.92.043022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2014] [Indexed: 06/05/2023]
Abstract
The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed.
Collapse
|
24
|
Fouxon I, Park Y, Harduf R, Lee C. Inhomogeneous distribution of water droplets in cloud turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:033001. [PMID: 26465550 DOI: 10.1103/physreve.92.033001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2014] [Indexed: 06/05/2023]
Abstract
We consider sedimentation of small particles in the turbulent flow where fluid accelerations are much smaller than acceleration of gravity g. The particles are dragged by the flow by linear friction force. We demonstrate that the pair-correlation function of particles' concentration diverges with decreasing separation as a power law with negative exponent. This manifests fractal distribution of particles in space. We find that the exponent is proportional to ratio of integral of energy spectrum of turbulence times the wave number over g. The proportionality coefficient is a universal number independent of particle size. We derive the spectrum of Lyapunov exponents that describes the evolution of small patches of particles. It is demonstrated that particles separate dominantly in the horizontal plane. This provides a theory for the recently observed vertical columns formed by the particles. We confirm the predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include conditions that hold for water droplets in warm clouds thus providing a tool for the prediction of rain formation.
Collapse
Affiliation(s)
- Itzhak Fouxon
- Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, South Korea
| | - Yongnam Park
- Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea
| | - Roei Harduf
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Changhoon Lee
- Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, South Korea
- Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea
| |
Collapse
|
25
|
De Pietro M, van Hinsberg MAT, Biferale L, Clercx HJH, Perlekar P, Toschi F. Clustering of vertically constrained passive particles in homogeneous isotropic turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:053002. [PMID: 26066244 DOI: 10.1103/physreve.91.053002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2014] [Indexed: 06/04/2023]
Abstract
We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale η, that maximizes the clustering of the particles.
Collapse
Affiliation(s)
- Massimo De Pietro
- Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Università "Tor Vergata," Via della Ricerca Scientifica 1, I-00133 Roma, Italy
| | - Michel A T van Hinsberg
- Department of Applied Physics, J. M. Burgerscentrum, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Luca Biferale
- Dipartimento di Fisica and Istituto Nazionale di Fisica Nucleare, Università "Tor Vergata," Via della Ricerca Scientifica 1, I-00133 Roma, Italy
| | - Herman J H Clercx
- Department of Applied Physics, J. M. Burgerscentrum, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Prasad Perlekar
- TIFR Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Federico Toschi
- Department of Applied Physics and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands and IAC, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, I-00185 Roma, Italy
| |
Collapse
|
26
|
Farhan M, Nicolleau FCGA, Nowakowski AF. Effect of gravity on clustering patterns and inertial particle attractors in kinematic simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:043021. [PMID: 25974594 DOI: 10.1103/physreve.91.043021] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Indexed: 06/04/2023]
Abstract
In this paper, we study the clustering of inertial particles using a periodic kinematic simulation. The systematic Lagrangian tracking of particles makes it possible to identify the particles' clustering patterns for different values of particle inertia and drift velocity. The different cases are characterized by different pairs of Stokes number (St) and Froude number (Fr). For the present study, 0≤St≤1 and 0.4≤Fr≤1.4. The main focus is to identify and then quantify the clustering attractor-when it exists-that is the set of points in the physical space where the particles settle when time goes to infinity. Depending on the gravity effect and inertia values, the Lagrangian attractor can have different dimensions, varying from the initial three-dimensional space to two-dimensional layers and one-dimensional attractors that can be shifted from a horizontal to a vertical position.
Collapse
Affiliation(s)
- M Farhan
- Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom
| | - F C G A Nicolleau
- Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom
| | - A F Nowakowski
- Sheffield Fluid Mechanics Group, Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom
| |
Collapse
|