1
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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.
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Affiliation(s)
- Priyanka Maity
- Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany
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2
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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.
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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
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3
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Almerol JLO, Liponhay MP. Clustering of fast gyrotactic particles in low-Reynolds-number flow. PLoS One 2022; 17:e0266611. [PMID: 35390073 PMCID: PMC8989315 DOI: 10.1371/journal.pone.0266611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 03/23/2022] [Indexed: 11/18/2022] Open
Abstract
Systems of particles in turbulent flows exhibit clustering where particles form patches in certain regions of space. Previous studies have shown that motile particles accumulate inside the vortices and in downwelling regions, while light and heavy non-motile particles accumulate inside and outside the vortices, respectively. While strong clustering is generated in regions of high vorticity, clustering of motile particles is still observed in fluid flows where vortices are short-lived. In this study, we investigate the clustering of fast swimming particles in a low-Reynolds-number turbulent flow and characterize the probability distributions of particle speed and acceleration and their influence on particle clustering. We simulate gyrotactic swimming particles in a cubic system with homogeneous and isotropic turbulent flow. Here, the swimming velocity explored is relatively faster than what has been explored in other reports. The fluid flow is produced by conducting a direct numerical simulation of the Navier-Stokes equation. In contrast with the previous results, our results show that swimming particles can accumulate outside the vortices, and clustering is dictated by the swimming number and is invariant with the stability number. We have also found that highly clustered particles are sufficiently characterized by their acceleration, where the increase in the acceleration frequency distribution of the most clustered particles suggests a direct influence of acceleration on clustering. Furthermore, the acceleration of the most clustered particles resides in acceleration values where a cross-over in the acceleration PDFs are observed, an indicator that particle acceleration generates clustering. Our findings on motile particles clustering can be applied to understanding the behavior of faster natural or artificial swimmers.
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Affiliation(s)
| | - Marissa Pastor Liponhay
- Analytics, Computing, and Complex Systems laboratory (ACCeSs@AIM), Asian Insitute of Management, Makati City, Philippines
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4
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Samant O, Alageshan JK, Sharma S, Kuley A. Dynamic mode decomposition of inertial particle caustics in Taylor-Green flow. Sci Rep 2021; 11:10456. [PMID: 34001985 PMCID: PMC8128860 DOI: 10.1038/s41598-021-89953-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 04/29/2021] [Indexed: 11/16/2022] Open
Abstract
Inertial particles advected by a background flow can show complex structures. We consider inertial particles in a 2D Taylor-Green (TG) flow and characterize particle dynamics as a function of the particle's Stokes number using dynamic mode decomposition (DMD) method from particle image velocimetry (PIV) like-data. We observe the formation of caustic structures and analyze them using DMD to (a) determine the Stokes number of the particles, and (b) estimate the particle Stokes number composition. Our analysis in this idealized flow will provide useful insight to analyze inertial particles in more complex or turbulent flows. We propose that the DMD technique can be used to perform similar analysis on an experimental system.
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Affiliation(s)
- Omstavan Samant
- Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, UK
| | | | | | - Animesh Kuley
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
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5
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van den Wildenberg S, Jia X, Roche O. Acoustic probing of the particle concentration in turbulent granular suspensions in air. Sci Rep 2020; 10:16544. [PMID: 33024148 PMCID: PMC7538992 DOI: 10.1038/s41598-020-73427-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 09/08/2020] [Indexed: 11/09/2022] Open
Abstract
Dilute gas-particle suspensions in which the particles are carried by the fluid are found in various industrial and geophysical contexts. One fundamental issue that limits our understanding of such systems is the difficulty to obtain information on the particle concentration inside these often optically opaque suspensions. To overcome this difficulty, we develop ultrasonic spectroscopy to monitor the local particle concentration [Formula: see text] of glass particles (with diameters [Formula: see text] 77 [Formula: see text]m or 155 [Formula: see text]m) suspended in air. First, we determine the minimal air velocity, [Formula: see text], necessary to suspend the particles from the maximum decrease in the transmitted wave amplitude and velocity of ultrasound propagating through the suspension. Next, setting the air velocity at [Formula: see text], we increase the mass of particles and monitor acoustically the local solid volume fraction, [Formula: see text], by measuring the ultrasound wave attenuation coefficient and phase velocity as a function of frequency on the basis of classical scattering and hydrodynamic models. For the frequency ranges and suspensions considered here, the viscous dissipation dominates over scattering and thermal conduction losses. We show that, for a characteristic air velocity [Formula: see text], the locally measured [Formula: see text] reaches a critical value, in agreement with a recent study on turbulent gas-particle mixtures. Moreover, we find that this critical [Formula: see text] increases with the size of the particles. Finally, analysis of the temporal fluctuations of the locally measured solid volume fraction, suggests that high density regions (clusters) are present even in suspensions with concentrations below the critical concentration. This differs from the current hypothesis according to which the critical concentration coincides with the onset of cluster formation.
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Affiliation(s)
- S van den Wildenberg
- Université Clermont Auvergne, CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, 63000, Clermont-Ferrand, France.
| | - X Jia
- Institut Langevin, ESPCI Paris, PSL University, CNRS, 75005, Paris, France
| | - O Roche
- Université Clermont Auvergne, CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, 63000, Clermont-Ferrand, France
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6
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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: 1] [Impact Index Per Article: 0.3] [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.
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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
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7
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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.
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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
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8
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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.
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Affiliation(s)
- Akshay Bhatnagar
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
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9
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Buzzicotti M, Biferale L, Toschi F. Statistical Properties of Turbulence in the Presence of a Smart Small-Scale Control. PHYSICAL REVIEW LETTERS 2020; 124:084504. [PMID: 32167371 DOI: 10.1103/physrevlett.124.084504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Accepted: 01/06/2020] [Indexed: 06/10/2023]
Abstract
By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a nonlinear extra viscosity acting preferentially on high vorticity regions. We show that the presence of such smart small-scale drag can strongly reduce intermittency and non-Gaussian fluctuations. Our results pave the way towards a deeper understanding on the fundamental role of degrees of freedom in turbulence as well as on the impact of (pseudo)coherent structures on the statistical small-scale properties. Our work can be seen as a first attempt to develop smart-Lagrangian forcing or drag mechanisms to control turbulence.
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Affiliation(s)
- Michele Buzzicotti
- Department of Physics and INFN, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Luca Biferale
- Department of Physics and INFN, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Federico Toschi
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands and Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy
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10
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Battista F, Mollicone JP, Gualtieri P, Messina R, Casciola C. Exact regularized point particle (ERPP) method for particle-laden wall-bounded flows in the two-way coupling regime. JOURNAL OF FLUID MECHANICS 2019; 878:420-444. [PMID: 32879533 PMCID: PMC7116011 DOI: 10.1017/jfm.2019.622] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The Exact Regularized Point Particle (ERPP) method is extended to treat the interphase momentum coupling between particles and fluid in the presence of walls by accounting for the vorticity generation due to the particles close to solid boundaries. The ERPP method overcomes the limitations of other methods by allowing the simulation of an extensive parameter space (Stokes number, mass loading, particle-to-fluid density ratio and Reynolds number) and of particle spatial distributions that are uneven (few particles per computational cell). The enhanced ERPP method is explained in detail and validated by considering the global impulse balance. In conditions when particles are located close to the wall, a common scenario in wall-bounded turbulent flows, the main contribution to the total impulse arises from the particle-induced vorticity at the solid boundary. The method is applied to direct numerical simulations of particle-laden turbulent pipe flow in the two-way coupling regime to address the turbulence modulation. The effects of the mass loading, the Stokes number and the particle-to-fluid density ratio are investigated. The drag is either unaltered or increased by the particles with respect to the uncoupled case. No drag reduction is found in the parameter space considered. The momentum stress budget, which includes an extra stress contribution by the particles, provides the rationale behind the drag behaviour. The extra stress produces a momentum flux towards the wall that strongly modifies the viscous stress, the culprit of drag at solid boundaries.
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Affiliation(s)
- F. Battista
- ENEA, Italian Agency for New Technologies, Energy and Sustainable Economic Development, via Anguillarese 301, 00123 Rome, Italy
| | - J.-P. Mollicone
- Department of Civil and Environmental Engineering, Imperial College London, United Kingdom
| | - P. Gualtieri
- Department of Mechanical and Aerospace Engineering Sapienza University of Rome via Eudossiana 18, 00184 Rome, Italy
| | - R. Messina
- Department of Mechanical and Aerospace Engineering Sapienza University of Rome via Eudossiana 18, 00184 Rome, Italy
| | - C.M. Casciola
- Department of Mechanical and Aerospace Engineering Sapienza University of Rome via Eudossiana 18, 00184 Rome, Italy
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11
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Biferale L, Bonaccorso F, Buzzicotti M, Clark Di Leoni P, Gustavsson K. Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning. CHAOS (WOODBURY, N.Y.) 2019; 29:103138. [PMID: 31675828 DOI: 10.1063/1.5120370] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 10/03/2019] [Indexed: 05/20/2023]
Abstract
To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel that has a slip velocity with fixed intensity, Vs, but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasioptimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process and are, therefore, not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when Vs is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.
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Affiliation(s)
- L Biferale
- Department of Physics, INFN University of Rome Tor vergata, via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - F Bonaccorso
- Department of Physics, INFN University of Rome Tor vergata, via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Buzzicotti
- Department of Physics, INFN University of Rome Tor vergata, via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - P Clark Di Leoni
- Department of Physics, INFN University of Rome Tor vergata, via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - K Gustavsson
- Department of Physics, University of Gothenburg, Gothenburg 41296, Sweden
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12
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Pandey V, Perlekar P, Mitra D. Clustering and energy spectra in two-dimensional dusty gas turbulence. Phys Rev E 2019; 100:013114. [PMID: 31499820 DOI: 10.1103/physreve.100.013114] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Indexed: 11/07/2022]
Abstract
We present direct numerical simulation of heavy inertial particles (dust) immersed in two-dimensional turbulent flow (gas). The dust particles are modeled as monodispersed heavy particles capable of modifying the flow through two-way coupling. By varying the Stokes number (St) and the mass-loading parameter (ϕ_{m}), we study the clustering phenomenon and the gas phase kinetic energy spectra. We find that the dust-dust correlation dimension (d_{2}) also depends on ϕ_{m}. In particular, clustering decreases as mass loading (ϕ_{m}) is increased. In the kinetic energy spectra of gas we show (i) the emergence of a different scaling regime and that (ii) the scaling exponent in this regime is not universal but a function of both St and ϕ_{m}. Using a scale-by-scale enstrophy budget analysis we show that in this emerged scaling regime, which we call the dust-dissipative range, viscous dissipation due to the gas balances the back-reaction from the dust.
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Affiliation(s)
- Vikash Pandey
- TIFR Centre for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Prasad Perlekar
- TIFR Centre for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Dhrubaditya Mitra
- NORDITA, Royal Institute of Technology and Stockholm University, SE-10691 Stockholm, Sweden
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13
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Cencini M, Boffetta G, Borgnino M, De Lillo F. Gyrotactic phytoplankton in laminar and turbulent flows: A dynamical systems approach. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:31. [PMID: 30879226 DOI: 10.1140/epje/i2019-11792-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Accepted: 02/08/2019] [Indexed: 06/09/2023]
Abstract
Gyrotactic algae are bottom heavy, motile cells whose swimming direction is determined by a balance between a buoyancy torque directing them upwards and fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic model for phytoplankton motility in flows. The essential attractiveness of this peculiar form of motility is the availability of a mechanistic description which, despite its simplicity, revealed predictive, rich in phenomenology, easily complemented to include the effects of shape, feedback on the fluid and stochasticity (e.g., in cell orientation). In this review we consider recent theoretical, numerical and experimental results to discuss how, depending on flow properties, gyrotaxis can produce inhomogeneous phytoplankton distributions on a wide range of scales, from millimeters to kilometers, in both laminar and turbulent flows. In particular, we focus on the phenomenon of gyrotactic trapping in nonlinear shear flows and in fractal clustering in turbulent flows. We shall demonstrate the usefulness of ideas and tools borrowed from dynamical systems theory in explaining and interpreting these phenomena.
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Affiliation(s)
- Massimo Cencini
- Istituto dei Sistemi Complessi, CNR, via dei Taurini 19, 00185, Roma, Italy
- INFN Tor Vergata, via della Ricerca Scientifica 1, 00133, Roma, Italy
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125, Torino, Italy
| | - Matteo Borgnino
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125, Torino, Italy
| | - Filippo De Lillo
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125, Torino, Italy.
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14
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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.
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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
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15
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Ariki T, Yoshida K, Matsuda K, Yoshimatsu K. Scale-similar clustering of heavy particles in the inertial range of turbulence. Phys Rev E 2018; 97:033109. [PMID: 29776089 DOI: 10.1103/physreve.97.033109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Indexed: 05/28/2023]
Abstract
Heavy particle clustering in turbulence is discussed from both phenomenological and analytical points of view, where the -4/3 power law of the pair-correlation function is obtained in the inertial range. A closure theory explains the power law in terms of the balance between turbulence mixing and preferential-concentration mechanism. The obtained -4/3 power law is supported by a direct numerical simulation of particle-laden turbulence.
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Affiliation(s)
- Taketo Ariki
- Institute of Materials and Systems for Sustainability, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
| | - Kyo Yoshida
- Division of Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba 305-8571, Japan
| | - Keigo Matsuda
- Center for Earth Information Science and Technology, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama 236-0001, Japan
| | - Katsunori Yoshimatsu
- Institute of Materials and Systems for Sustainability, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
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16
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Bhatnagar A, Gustavsson K, Mitra D. Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles. Phys Rev E 2018; 97:023105. [PMID: 29548076 DOI: 10.1103/physreve.97.023105] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Indexed: 11/07/2022]
Abstract
We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component V_{R} for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D_{2}. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011)PLEEE81539-375510.1103/PhysRevE.84.045304; J. Turbul. 15, 34 (2014)1468-524810.1080/14685248.2013.875188] that the scale invariant part of the distribution has two asymptotic regimes: (1) |V_{R}|≪R, where the distribution depends solely on R, and (2) |V_{R}|≫R, where the distribution is a function of |V_{R}| alone. The probability distributions in these two regimes are matched along a straight line: |V_{R}|=z^{*}R. Our simulations confirm that this is indeed correct. We further obtain D_{2} and z^{*} as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St.
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Affiliation(s)
- Akshay Bhatnagar
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| | - K Gustavsson
- Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden
| | - Dhrubaditya Mitra
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
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17
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Das S, Gupte N. Transport, diffusion, and energy studies in the Arnold-Beltrami-Childress map. Phys Rev E 2018; 96:032210. [PMID: 29346902 DOI: 10.1103/physreve.96.032210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Indexed: 11/07/2022]
Abstract
We study the transport and diffusion properties of passive inertial particles described by a six-dimensional dissipative bailout embedding map. The base map chosen for the study is the three-dimensional incompressible Arnold-Beltrami-Childress (ABC) map chosen as a representation of volume preserving flows. There are two distinct cases: the two-action and the one-action cases, depending on whether two or one of the parameters (A,B,C) exceed 1. The embedded map dynamics is governed by two parameters (α,γ), which quantify the mass density ratio and dissipation, respectively. There are important differences between the aerosol (α<1) and the bubble (α>1) regimes. We have studied the diffusive behavior of the system and constructed the phase diagram in the parameter space by computing the diffusion exponents η. Three classes have been broadly classified-subdiffusive transport (η<1), normal diffusion (η≈1), and superdiffusion (η>1) with η≈2 referred to as the ballistic regime. Correlating the diffusive phase diagram with the phase diagram for dynamical regimes seen earlier, we find that the hyperchaotic bubble regime is largely correlated with normal and superdiffusive behavior. In contrast, in the aerosol regime, ballistic superdiffusion is seen in regions that largely show periodic dynamical behaviors, whereas subdiffusive behavior is seen in both periodic and chaotic regimes. The probability distributions of the diffusion exponents show power-law scaling for both aerosol and bubbles in the superdiffusive regimes. We further study the Poincáre recurrence times statistics of the system. Here, we find that recurrence time distributions show power law regimes due to the existence of partial barriers to transport in the phase space. Moreover, the plot of average particle kinetic energies versus the mass density ratio for the two-action case exhibits a devil's staircase-like structure for higher dissipation values. We explain these results and discuss their implications for realistic systems.
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Affiliation(s)
- Swetamber Das
- Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - Neelima Gupte
- Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India
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18
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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.
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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
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19
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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.
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20
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Cecconi F, Puglisi A, Sarracino A, Vulpiani A. Anomalous force-velocity relation of driven inertial tracers in steady laminar flows. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:81. [PMID: 28942558 DOI: 10.1140/epje/i2017-11571-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 09/08/2017] [Indexed: 06/07/2023]
Abstract
We study the nonlinear response to an external force of an inertial tracer advected by a two-dimensional incompressible laminar flow and subject to thermal noise. In addition to the driving external field F, the main parameters in the system are the noise amplitude [Formula: see text] and the characteristic Stokes time [Formula: see text] of the tracer. The relation velocity vs. force shows interesting effects, such as negative differential mobility (NDM), namely a non-monotonic behavior of the tracer velocity as a function of the applied force, and absolute negative mobility (ANM), i.e. a net motion against the bias. By extensive numerical simulations, we investigate the phase chart in the parameter space of the model, [Formula: see text], identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.
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Affiliation(s)
- F Cecconi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185, Roma, Italy
| | - A Puglisi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185, Roma, Italy
| | - A Sarracino
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185, Roma, Italy.
| | - A Vulpiani
- Dipartimento di Fisica, Sapienza Università di Roma, and CNR-ISC, p.le A. Moro 2, 0018, Roma, Italy
- Accademia dei Lincei, Centro Interdisciplinare B. Segre, Roma, Italy
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21
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Liberman M, Kleeorin N, Rogachevskii I, Haugen NEL. Mechanism of unconfined dust explosions: Turbulent clustering and radiation-induced ignition. Phys Rev E 2017; 95:051101. [PMID: 28618553 DOI: 10.1103/physreve.95.051101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/07/2023]
Abstract
It is known that unconfined dust explosions typically start off with a relatively weak primary flame followed by a severe secondary explosion. We show that clustering of dust particles in a temperature stratified turbulent flow ahead of the primary flame may give rise to a significant increase in the radiation penetration length. These particle clusters, even far ahead of the flame, are sufficiently exposed and heated by the radiation from the flame to become ignition kernels capable to ignite a large volume of fuel-air mixtures. This efficiently increases the total flame surface area and the effective combustion speed, defined as the rate of reactant consumption of a given volume. We show that this mechanism explains the high rate of combustion and overpressures required to account for the observed level of damage in unconfined dust explosions, e.g., at the 2005 Buncefield vapor-cloud explosion. The effect of the strong increase of radiation transparency due to turbulent clustering of particles goes beyond the state of the art of the application to dust explosions and has many implications in atmospheric physics and astrophysics.
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Affiliation(s)
- Michael Liberman
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
| | - Nathan Kleeorin
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
- Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
| | - Igor Rogachevskii
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
- Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
| | - Nils Erland L Haugen
- SINTEF Energy Research, 7034 Trondheim, Norway
- Department of Energy and Process Engineering, Norwegian University of Science and Technology, Kolbjørn Hejes vei 1B, 7491 Trondheim, Norway
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22
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Hartlep T, Cuzzi JN, Weston B. Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence. Phys Rev E 2017; 95:033115. [PMID: 28415324 DOI: 10.1103/physreve.95.033115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Indexed: 11/07/2022]
Abstract
Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into subvolumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik and Alipchenkov [New J. Phys. 11, 103018 (2009)NJOPFM1367-263010.1088/1367-2630/11/10/103018]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.
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Affiliation(s)
- Thomas Hartlep
- Bay Area Environmental Research Institute, Petaluma, California 94952, USA
| | - Jeffrey N Cuzzi
- NASA Ames Research Center, Moffett Field, California 94035, USA
| | - Brian Weston
- University of California Davis, Mechanical & Aerospace Engineering, Davis, California 95616, USA
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23
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Gunther T, Theisel H. Backward Finite-Time Lyapunov Exponents in Inertial Flows. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2017; 23:970-979. [PMID: 27875210 DOI: 10.1109/tvcg.2016.2599016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Inertial particles are finite-sized objects that are carried by fluid flows and in contrast to massless tracer particles they are subject to inertia effects. In unsteady flows, the dynamics of tracer particles have been extensively studied by the extraction of Lagrangian coherent structures (LCS), such as hyperbolic LCS as ridges of the Finite-Time Lyapunov Exponent (FTLE). The extension of the rich LCS framework to inertial particles is currently a hot topic in the CFD literature and is actively under research. Recently, backward FTLE on tracer particles has been shown to correlate with the preferential particle settling of small inertial particles. For larger particles, inertial trajectories may deviate strongly from (massless) tracer trajectories, and thus for a better agreement, backward FTLE should be computed on inertial trajectories directly. Inertial backward integration, however, has not been possible until the recent introduction of the influence curve concept, which - given an observation and an initial velocity - allows to recover all sources of inertial particles as tangent curves of a derived vector field. In this paper, we show that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles. We further generalize the influence curve concept to general equations of motion in unsteady spatio-velocity phase spaces, which enables backward integration with more general equations of motion. Applying the influence curve concept to tracer particles in the spatio-velocity domain emits streaklines in massless flows as tangent curves of the influence curve vector field. We demonstrate the correlation between inertial backward FTLE and the preferential particle settling in a number of unsteady vector fields.
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24
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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.
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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
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25
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Sarracino A, Cecconi F, Puglisi A, Vulpiani A. Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility. PHYSICAL REVIEW LETTERS 2016; 117:174501. [PMID: 27824440 DOI: 10.1103/physrevlett.117.174501] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Indexed: 06/06/2023]
Abstract
We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive numerical simulations, that the force-velocity relation for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negative differential and absolute mobility. These effects rely upon a subtle coupling between inertia and applied force that induces the tracer to persist in particular regions of phase space with a velocity opposite to the force. The relevance of this coupling is revisited in the framework of nonequilibrium response theory, applying a generalized Einstein relation to our system. The possibility of experimental observation of these results is also discussed.
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Affiliation(s)
- A Sarracino
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
| | - F Cecconi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
| | - A Puglisi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
| | - A Vulpiani
- Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy
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26
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Bocanegra Evans H, Dam N, Bertens G, van der Voort D, van de Water W. Dispersion of Droplet Clouds in Turbulence. PHYSICAL REVIEW LETTERS 2016; 117:164501. [PMID: 27792377 DOI: 10.1103/physrevlett.117.164501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2015] [Indexed: 06/06/2023]
Abstract
We measure the absolute dispersion of clouds of monodisperse, phosphorescent droplets in turbulent air by means of high-speed image-intensified video recordings. Laser excitation allows the initial preparation of well-defined, pencil-shaped luminous droplet clouds in a completely nonintrusive way. We find that the dispersion of the clouds is faster than the dispersion of fluid elements. We speculate that preferential concentration of inertial droplet clouds is responsible for the enhanced dispersion.
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Affiliation(s)
- Humberto Bocanegra Evans
- Physics Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Nico Dam
- Mechanical Engineering Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Guus Bertens
- Physics Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Dennis van der Voort
- Physics Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Willem van de Water
- Physics Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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27
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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).
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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
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28
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Schmidt L, Fouxon I, Krug D, van Reeuwijk M, Holzner M. Clustering of particles in turbulence due to phoresis. Phys Rev E 2016; 93:063110. [PMID: 27415361 DOI: 10.1103/physreve.93.063110] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Indexed: 04/13/2023]
Abstract
We demonstrate that diffusiophoretic, thermophoretic, and chemotactic phenomena in turbulence lead to clustering of particles on multifractal sets that can be described using one single framework, valid when the particle size is much smaller than the smallest length scale of turbulence l_{0}. To quantify the clustering, we derive positive pair correlations and fractal dimensions that hold for scales smaller than l_{0}. For scales larger than l_{0} the pair-correlation function is predicted to show a stretched exponential decay towards 1. In the case of inhomogeneous turbulence we find that the fractal dimension depends on the direction of inhomogeneity. By performing experiments with particles in a turbulent gravity current we demonstrate clustering induced by salinity gradients in conformity to the theory. The particle size in the experiment is comparable to l_{0}, outside the strict validity region of the theory, suggesting that the theoretical predictions transfer to this practically relevant regime. This clustering mechanism may provide the key to the understanding of a multitude of processes such as formation of marine snow in the ocean and population dynamics of chemotactic bacteria.
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Affiliation(s)
- Lukas Schmidt
- ETH Zurich, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland
| | - Itzhak Fouxon
- ETH Zurich, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland
- Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, South Korea
| | - Dominik Krug
- Department of Mechanical Engineering, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Maarten van Reeuwijk
- Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, United Kingdom
| | - Markus Holzner
- ETH Zurich, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland
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29
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Sudharsan M, Brunton SL, Riley JJ. Lagrangian coherent structures and inertial particle dynamics. Phys Rev E 2016; 93:033108. [PMID: 27078448 DOI: 10.1103/physreve.93.033108] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Indexed: 06/05/2023]
Abstract
In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.
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Affiliation(s)
- M Sudharsan
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
| | - Steven L Brunton
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
- Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2420, USA
| | - James J Riley
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA
- Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2420, USA
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30
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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.
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31
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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.
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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
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32
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Bragg AD, Ireland PJ, Collins LR. Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:023029. [PMID: 26382525 DOI: 10.1103/physreve.92.023029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2014] [Indexed: 06/05/2023]
Abstract
In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str≪1, where Str is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When Str≳O(1) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014)]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the "sweep-stick" mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009)]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str≪1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov [Phys. Fluids 19, 113308 (2007)] and use this, together with the results from our analysis, to predict the analytic form of the RDF in the inertial range for Str1, which, unlike that in the dissipation range, is not scale invariant. The results are in good agreement with direct numerical simulations, provided the separations are well within the inertial range.
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Affiliation(s)
- Andrew D Bragg
- Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Peter J Ireland
- Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Lance R Collins
- Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
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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.
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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
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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.
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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
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Bec J, Homann H, Krstulovic G. Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles. PHYSICAL REVIEW LETTERS 2014; 112:234503. [PMID: 24972213 DOI: 10.1103/physrevlett.112.234503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2014] [Indexed: 06/03/2023]
Abstract
Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong frontlike discontinuities. This novel effect is responsible for extremely high levels of fluctuations for the passive field sampled by the particles that impacts the heat fluxes exchanged between the particles and the surrounding fluid. Instantaneous and averaged heat fluxes are shown to follow strongly intermittent statistics and anomalous scaling laws.
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Affiliation(s)
- Jérémie Bec
- Laboratoire Lagrange, UMR7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d'Azur, CS 34229, 06304 Nice Cedex 4, France
| | - Holger Homann
- Laboratoire Lagrange, UMR7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d'Azur, CS 34229, 06304 Nice Cedex 4, France
| | - Giorgio Krstulovic
- Laboratoire Lagrange, UMR7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d'Azur, CS 34229, 06304 Nice Cedex 4, France
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Bec J, Homann H, Ray SS. Gravity-driven enhancement of heavy particle clustering in turbulent flow. PHYSICAL REVIEW LETTERS 2014; 112:184501. [PMID: 24856699 DOI: 10.1103/physrevlett.112.184501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2014] [Indexed: 06/03/2023]
Abstract
Heavy particles suspended in a turbulent flow settle faster than in a still fluid. This effect stems from a preferential sampling of the regions where the fluid flows downward and is quantified here as a function of the level of turbulence, of particle inertia, and of the ratio between gravity and turbulent accelerations. By using analytical methods and detailed, state-of-the-art numerical simulations, settling is shown to induce an effective horizontal two-dimensional dynamics that increases clustering and reduce relative velocities between particles. These two competing effects can either increase or decrease the geometrical collision rates between same-size particles and are crucial for realistic modeling of coalescing particles.
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Affiliation(s)
- Jérémie Bec
- Laboratoire Lagrange, Université de Nice-Sophia Antipolis, CNRS, OCA, Boulevard de l'Observatoire, 06300 Nice, France
| | - Holger Homann
- Laboratoire Lagrange, Université de Nice-Sophia Antipolis, CNRS, OCA, Boulevard de l'Observatoire, 06300 Nice, France
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India
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De Lillo F, Cencini M, Durham WM, Barry M, Stocker R, Climent E, Boffetta G. Turbulent fluid acceleration generates clusters of gyrotactic microorganisms. PHYSICAL REVIEW LETTERS 2014; 112:044502. [PMID: 24580457 DOI: 10.1103/physrevlett.112.044502] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2013] [Indexed: 06/03/2023]
Abstract
The motility of microorganisms is often biased by gradients in physical and chemical properties of their environment, with myriad implications on their ecology. Here we show that fluid acceleration reorients gyrotactic plankton, triggering small-scale clustering. We experimentally demonstrate this phenomenon by studying the distribution of the phytoplankton Chlamydomonas augustae within a rotating tank and find it to be in good agreement with a new, generalized model of gyrotaxis. When this model is implemented in a direct numerical simulation of turbulent flow, we find that fluid acceleration generates multifractal plankton clustering, with faster and more stable cells producing stronger clustering. By producing accumulations in high-vorticity regions, this process is fundamentally different from clustering by gravitational acceleration, expanding the range of mechanisms by which turbulent flows can impact the spatial distribution of active suspensions.
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Affiliation(s)
- Filippo De Lillo
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Massimo Cencini
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via dei Taurini 19, 00185 Rome, Italy
| | - William M Durham
- Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, United Kingdom
| | - Michael Barry
- Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Roman Stocker
- Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Eric Climent
- Institut de Mécanique des Fluides, Université de Toulouse, INPT-UPS-CNRS, Allée du Pr. Camille Soula, F-31400 Toulouse, France
| | - Guido Boffetta
- Dipartimento di Fisica and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
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Durham WM, Climent E, Barry M, De Lillo F, Boffetta G, Cencini M, Stocker R. Turbulence drives microscale patches of motile phytoplankton. Nat Commun 2013; 4:2148. [DOI: 10.1038/ncomms3148] [Citation(s) in RCA: 212] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2013] [Accepted: 06/13/2013] [Indexed: 11/09/2022] Open
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Bec J, Musacchio S, Ray SS. Sticky elastic collisions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063013. [PMID: 23848778 DOI: 10.1103/physreve.87.063013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2013] [Indexed: 06/02/2023]
Abstract
The effects of purely elastic collisions on the dynamics of heavy inertial particles are investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of interparticle separations and relative velocities are strongly influenced by the occurrence of sticky elastic collisions-particle pairs undergo a large number of collisions against each other during a small time interval over which, hence, they remain close to each other. A theoretical framework is provided for describing and quantifying this phenomenon and it is substantiated by numerical simulations. Furthermore, the impact of hydrodynamic interactions is discussed for such a system of colliding particles.
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Affiliation(s)
- Jérémie Bec
- Laboratoire Lagrange, UMR 7293, Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d'Azur, Bd. de l'Observatoire, 06300 Nice, France
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Bianco F, Chibbaro S, Vergni D, Vulpiani A. Front speed in reactive compressible stirred media. Phys Rev E 2013; 87:042924. [PMID: 23679506 DOI: 10.1103/physreve.87.042924] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Indexed: 11/07/2022]
Abstract
We investigated a nonlinear advection-diffusion-reaction equation for a passive scalar field. The purpose is to understand how the compressibility can affect the front dynamics and the bulk burning rate. We study two classes of flows: periodic shear flow and cellular flow, analyzing the system by varying the extent of compressibility and the reaction rate. We find that the bulk burning rate v(f) in a shear flow increases with compressibility intensity ε, following the relation Δv(f)~ε(2). Furthermore, the faster the reaction is, the more important the difference is with respect to the laminar case. The effect has been quantitatively measured, and it turns out to be generally small. For the cellular flow, two extreme cases have been investigated, with the whole perturbation situated either in the center of the vortex or in the periphery. The dependence in this case does not show a monotonic scaling with different behavior in the two cases. The enhancing remains modest and is always less than 20%.
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Affiliation(s)
- Federico Bianco
- Institut D'Alembert, University Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 5, France
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41
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Jin G, Wang Y, Zhang J, He G. Turbulent Clustering of Point Particles and Finite-Size Particles in Isotropic Turbulent Flows. Ind Eng Chem Res 2013. [DOI: 10.1021/ie303507d] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guodong Jin
- LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Yun Wang
- LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Jian Zhang
- LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Guowei He
- LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, P. R. China
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Gustavsson K, Mehlig B. Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:023016. [PMID: 23496619 DOI: 10.1103/physreve.87.023016] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2012] [Revised: 09/13/2012] [Indexed: 06/01/2023]
Abstract
In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers, Ku, for arbitrary Stokes numbers, St. Our results are consistent with those obtained earlier in the limit Ku→0 and St→∞ such that Ku(2)St remains constant. We show how finite-time correlations and nonergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.
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Affiliation(s)
- K Gustavsson
- Department of Physics, Gothenburg University, 41296 Gothenburg, Sweden
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43
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Burgener T, Kadau D, Herrmann HJ. Clustering of inelastic soft spheres in homogeneous turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036321. [PMID: 23031027 DOI: 10.1103/physreve.86.036321] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2012] [Indexed: 06/01/2023]
Abstract
In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.
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Affiliation(s)
- Thomas Burgener
- Institute for Building Materials, ETH Zurich, 8093 Zürich, Switzerland.
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44
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Fiabane L, Zimmermann R, Volk R, Pinton JF, Bourgoin M. Clustering of finite-size particles in turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:035301. [PMID: 23030971 DOI: 10.1103/physreve.86.035301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2012] [Indexed: 06/01/2023]
Abstract
We investigate experimentally the spatial distributions of heavy and neutrally buoyant particles of finite size in a fully turbulent flow. Because their Stokes number (i.e., the ratio of the particle viscous relaxation time to a typical flow time scale) is close to unity, one may expect both classes of particles to aggregate in specific flow regions. This is not observed. Using a Voronoï analysis we show that neutrally buoyant particles sample turbulence homogeneously, whereas heavy particles do cluster. These results show that several dimensionless numbers are needed in the modeling (and understanding) of the behavior of particles entrained by turbulent motions.
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Affiliation(s)
- L Fiabane
- Laboratoire de Physique, ENS de Lyon, UMR CNRS 5672, Université de Lyon, France.
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45
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Fouxon I. Distribution of particles and bubbles in turbulence at a small Stokes number. PHYSICAL REVIEW LETTERS 2012; 108:134502. [PMID: 22540704 DOI: 10.1103/physrevlett.108.134502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2011] [Indexed: 05/31/2023]
Abstract
The inertia of particles driven by the turbulent flow of the surrounding fluid makes them prefer certain regions of the flow. The heavy particles lag behind the flow and tend to accumulate in the regions with less vorticity, while the light particles do the opposite. As a result of the long-time evolution, the particles distribute over a multifractal attractor in space. We consider this distribution using our recent results on the steady states of chaotic dynamics. We describe the preferential concentration analytically and derive the correlation functions of density and the fractal dimensions of the attractor. The results are obtained for real turbulence and are testable experimentally.
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Affiliation(s)
- Itzhak Fouxon
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel
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46
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Daitche A, Tél T. Memory effects are relevant for chaotic advection of inertial particles. PHYSICAL REVIEW LETTERS 2011; 107:244501. [PMID: 22243003 DOI: 10.1103/physrevlett.107.244501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2011] [Indexed: 05/31/2023]
Abstract
A systematic investigation of the effect of the history force on particle advection is carried out in a paradigmatic model flow of chaotic advection, the von Kármán flow. All investigated properties turn out to heavily depend on the presence of memory when compared to previous studies neglecting this force. We find a weaker tendency for accumulation and for caustics formation. The Lyapunov exponent of transients becomes larger, the escape rates are strongly altered. Attractors are found to be suppressed by the history force, and periodic ones have a very slow, t(-1/2)-type convergence towards the asymptotic form.
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Affiliation(s)
- Anton Daitche
- Institute for Theoretical Physics, Münster University, Wilhelm-Klemm-Straße 9, D-48149 Münster, Germany
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Burgener T, Kadau D, Herrmann HJ. Simulation of particle mixing in turbulent channel flow due to intrinsic fluid velocity fluctuation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:066301. [PMID: 21797471 DOI: 10.1103/physreve.83.066301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2010] [Indexed: 05/31/2023]
Abstract
We combine a discrete-element-method simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We find a linear increase of the mixing zone with the length of the pipe. Flows at different Reynolds number are studied. Below a critical Reynolds number at the Taylor microscale of around Rc ≈ 300 the mixing rate is strongly dependent on the Reynolds number. Above Rc the mixing rate stays nearly constant.
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Affiliation(s)
- Thomas Burgener
- Computational Physics, IfB, ETH-Hönggerberg, Schafmattstrasse 6, CH-8093 Zürich, Switzerland.
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Ilievski F, Mani M, Whitesides GM, Brenner MP. Self-assembly of magnetically interacting cubes by a turbulent fluid flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:017301. [PMID: 21405794 DOI: 10.1103/physreve.83.017301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2010] [Indexed: 05/30/2023]
Abstract
Previous work has demonstrated that combining mechanical vibration with magnetic interactions can result in the self-assembly of complex structures, albeit at low yield. Here we introduce a system where the yield of self-assembled structures is quantitatively predicted by a theoretical analysis. Millimeter-sized magnetic blocks, designed to form chains as their minimal energy state, are placed in a turbulent fluid flow. The distribution of chain lengths that form is quantitatively consistent with predictions, showing that the chain length distribution coincides with that of monomers or polymers in a thermal bath, with the turbulence strength parametrizing the effective temperature.
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Affiliation(s)
- Filip Ilievski
- Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138, USA
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Eidelman A, Elperin T, Kleeorin N, Melnik B, Rogachevskii I. Tangling clustering of inertial particles in stably stratified turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:056313. [PMID: 20866328 DOI: 10.1103/physreve.81.056313] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2009] [Revised: 03/08/2010] [Indexed: 05/29/2023]
Abstract
We have predicted theoretically and detected in laboratory experiments a tangling clustering of inertial particles in a stably stratified turbulence with imposed mean vertical temperature gradient. In the stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, i.e., the inertial particles are accumulated in the vicinity of the minimum of the mean temperature of the surrounding fluid, and a nonzero gradient of the mean particle number density, ∇N , is formed. It causes generation of fluctuations of the particle number density by tangling of the large-scale gradient ∇N by velocity fluctuations. In addition, the mean temperature gradient ∇T produces the temperature fluctuations by tangling of the large-scale gradient ∇T by velocity fluctuations. The anisotropic temperature fluctuations contribute to the two-point correlation function of the divergence of the particle velocity field, i.e., they increase the rate of formation of the particle clusters in small scales. We have demonstrated that in the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering (preferential concentration) that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter of ≈10 μm and Reynolds numbers based on turbulent length scale and rms velocity, Re=250 . In the experiments the correlation function for the inertial clustering in isothermal turbulence is much smaller than that for the tangling clustering in nonisothermal turbulence. The size of the tangling clusters is on the order of several Kolmogorov length scales. The clustering described in our study is found for inertial particles with small Stokes numbers and with the material density that is much larger than the fluid density. Our theoretical predictions are in a good agreement with the obtained experimental results.
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Affiliation(s)
- A Eidelman
- The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of Negev, PO Box 653, Beer-Sheva 84105, Israel.
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50
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Ijzermans RHA, Reeks MW, Meneguz E, Picciotto M, Soldati A. Measuring segregation of inertial particles in turbulence by a full Lagrangian approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:015302. [PMID: 19658760 DOI: 10.1103/physreve.80.015302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2008] [Indexed: 05/28/2023]
Abstract
Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the "full Lagrangian method." This is compared with the "mesoscopic Eulerian particle velocity field" both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, in contrast to the Eulerian, accurately predicts the compressibility of the particle velocity field even when the latter is characterized by singularities. In particular we use the method to evaluate the growth rates of spatial moments of the particle number density which reflect the fractal structure of segregation and the occurrence of singularities.
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Affiliation(s)
- R H A Ijzermans
- School of Mechanical and Systems Engineering, Newcastle University, Newcastle-upon-Tyne NE1 7RU, UK
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