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Acceleration of small heavy particles in homogeneous shear flow: direct numerical simulation and stochastic modelling of under-resolved intermittent turbulence

Published online by Cambridge University Press:  06 April 2020

A. Barge  and
M. A. Gorokhovski Open the ORCID record for M. A. Gorokhovski [Opens in a new window]
A. Barge
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon, CNRS-Université Claude Bernard Lyon 1-INSA Lyon, 69134Ecully, France
M. A. Gorokhovski*
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, École Centrale de Lyon, CNRS-Université Claude Bernard Lyon 1-INSA Lyon, 69134Ecully, France
*
†Email address for correspondence: mikhael.gorokhovski@ec-lyon.fr
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Abstract

The acceleration of inertial particles in a homogeneous shear flow may vigorously respond to the intense flow structures induced by the mean shear. In this study, by direct numerical simulation (DNS) of particle-laden shear flow, we observe the statistical properties of those accelerations, and then we assessed the recently proposed simulation approach in which the effect of intermittency on residual scales is linked directly with coarsely resolved flow turbulence. First, we focused on the acceleration statistics of fluid particles in a homogeneous shear flow. Consistent with previous findings in homogenous isotropic turbulence, the norm and the direction of fluid acceleration in shear flow are shown to be conditioned by the dynamics of intermittent long-lived vortical structures. The averaged acceleration norm of the fluid particle exhibits a pseudo-cyclic behaviour, which is a signature of the periodic action of the largest confined vortices against the mean shear. The long correlation time of the acceleration norm, of the order of the integral time, the high level of fluctuations of the acceleration norm (very close to the magnitude of the mean norm of acceleration) and the log-normality in its statistical distribution reflect the impact of intense flow structures in shear flow. The presence of these zones results also in highly non-Gaussian statistics of the acceleration of a fluid particle and its velocity increments at small time lags. Contrary to the acceleration norm, the acceleration direction of a fluid particle is observed to be short, of the order of the Kolmogorov time, and to be statistically independent of the acceleration norm. The short-time correlation of the acceleration direction is attributed usually to effects of centripetal forces in intense vorticity filaments. We suggest that, in homogeneous shear turbulence, there may be a supplementary effect on the acceleration direction: the vortex, stretched by the mean shear, may exert the preferential direction of fluid particle acceleration. As evidence, our DNS shows that fluid particles are accelerated preferentially in the direction of longitudinal vortical tubes, effectively stretched by the imposed mean shear. Concerning simulations with heavy point-wise particles, it is shown that, when the inertia of a particle is not high, its acceleration closely follows all the aforementioned properties of the fluid particle acceleration. Particularly, an inertial particle is also entrained by accelerating motion in the direction of the effectively stretched vortical tubes. Although with increasing Stokes number of the inertial particle, the effects of strong intermittency in the flow are filtered, it is shown that the alignment of the particle acceleration direction with vortical tubes is amplified – particles with higher inertia respond to solicitations of stronger vortical structures. An alternative to the Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465) preferential sweeping mechanism is discussed in this paper. When the shear turbulence is under-resolved, we employed the large-eddy simulation (LES) equations with a forcing term on the smallest resolved scales in order to simulate stochastically the effects of the dynamics on the residual scales. The forcing term is expressed with two independent stochastic processes, one for its norm and another for its direction. While the norm of acceleration is modelled using Pope’s log-normal process with the integral time for correlation, its direction is modelled in the framework of an Ornstein–Uhlenbeck process on the unit sphere. Consistently with our DNS, the latter process contains two presumed times: the homogeneous strain rate is specified as typical time of relaxation towards the direction of resolved vorticity, and the Kolmogorov time is presumed as a typical time of the diffusion process on the unit sphere. The high efficiency of this approach is demonstrated in prediction of the small-scale dynamics observed in DNS, even in the case when the shear length scale is not resolved by LES.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Turbulence simulation Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , A28
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Ahmed, A. M. & Elghobashi, S. 2001 Direct numerical simulation of particle dispersion in homogeneous turbulent shear flows. Phys. Fluids 13 (11), 3346–3364.CrossRefGoogle Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 2343–2353.CrossRefGoogle Scholar
Ayyalasomayajula, S., Gylafson, A., Collins, L. R., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid-generated wind tunnel turbulence. Phys. Rev. Lett. 97, 144507.CrossRefGoogle ScholarPubMed
Baggett, J. S., Jimenez, J. & Kravchenko, A. G. 1997 Resolution requirements in large-eddy simulation of shear-flow. In Center for Turbulence Research, Annual Research Briefs, pp. 51–66. Stanford University.Google Scholar
Barge, A. & Gorokhovski, M. A. 2019 Effects of regenerating cycle on Lagrangian acceleration in homogeneous shear flow. In Turbulent Cascades II ERCOFTAC Series, vol. 26, pp. 51–60. Springer (in review).CrossRefGoogle Scholar
Bassenne, M., Esmaily, M., Livescu, D., Moin, P. & Urzay, J. 2019 A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence. Intl J. Multiphase Flow 116, 270–280.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lamotte, A. & Toschi, F. 2010 Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536.CrossRefGoogle Scholar
Belin, F., Moisy, F., Tabeling, P. & Willaime, H. 1999 Worms in a turbulence experiment, from hot wire time series. In Fundamental Problematic Issues in Turbulence, pp. 129–140. Birkhäuser.CrossRefGoogle Scholar
Biferale, L. & Toschi, F. 2006 Joint statistics of acceleration and vorticity in fully developed turbulence. J. Turbul. 6 (40), 1–8.Google Scholar
Bourgoin, M. 2012 Habilitation a diriger des recherches: turbulent transport of particles and fields. University Joseph Fourier.Google Scholar
Chen, L., Coleman, S. W., Vassilicos, J. C. & Hu, Z. 2010 Acceleration in turbulent channel flow. J. Turbul. 11 (41), 1–23.Google Scholar
Chung, J. N. & Troutt, T. R. 1988 Simulation of a particle dispersion in an axisymmetric jet. J. Fluid Mech. 186, 199–222.CrossRefGoogle Scholar
Corrsin, S. 1958 Local isotropy in turbulent shear flow. NACA Res. Mem. 58B11.Google Scholar
Cottet, G.-H., Etancelin, J.-M., Perignon, F. & Picard, C. 2014 High order semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues. ESAIM: Math. Model. Numer. Anal. 48, 1029–1060.CrossRefGoogle Scholar
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows With Droplets and Particles. CRC Press.CrossRefGoogle Scholar
Domaradzki, J. A. & Adams, N. A. 2002 The subgrid-scale estimation model in the physical space. Phys. Fluids 11, 2330.CrossRefGoogle Scholar
Elsinga, G. E. & Marusic, I. 2010 Universal aspects of smallscale motions in turbulence. J. Fluid Mech. 662, 514–539.CrossRefGoogle Scholar
Fede, P. & Simonin, O. 2006 Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles. Phys. Fluids 18, 045103.CrossRefGoogle Scholar
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 3742.CrossRefGoogle Scholar
Gerashchenko, S., Sharp, N. S., Neuscamman, S. & Warhaft, Z. 2008 Lagrangian measurements of inertial particle accelerations in turbulent boundary layer. J. Fluid Mech. 617, 255–281.CrossRefGoogle Scholar
Ghate, A. S. & Lele, S. K. 2017 Subfilter-scale enrichment of planetary boundary layer large eddy simulation using discrete Fourrier-Gabor modes. J. Fluid Mech. 819, 494–539.CrossRefGoogle Scholar
Ghosal, S. 1999 Mathematical and physical constraints on large-eddy simulation of turbulence. AIAA J. 37 (4), 425–433.CrossRefGoogle Scholar
Gin, G., He, G. W. & Wang, L. P. 2010 Large eddy simulation of turbulent collision of heavy particles in isotropic turbulence. Phys. Fluids 22, 055106.Google Scholar
Gorokhovski, M. & Zamansky, R. 2018 Modeling the effects of small turbulent scales on the drag force for particles below and above the kolmogorov scale. Phys. Rev. Fluids 3 (3), 034602.CrossRefGoogle Scholar
Goto, S. 2008 A physical mechanism of the energy cascade in homogeneous isotropic turbulence. J. Fluid Mech. 605, 355–366.CrossRefGoogle Scholar
Gualtieri, P., Casciola, C. M., Benzi, R., Amati, G. & Piva, R. 2002 Scaling laws and intermittency in homogeneous shear flow. Phys. Fluids 14, 583.CrossRefGoogle Scholar
Gualtieri, P., Casciola, C. M., Benzi, R. & Piva, R. 2007 Preservation of statistical properties in large-eddy simulation of shear turbulence. J. Fluid Mech. 592, 471–494.CrossRefGoogle Scholar
Gualtieri, P., Picano, F. & Casciola, C. M. 2009 Anisotropic clustering of inertial particles in homogeneous shear flow. J. Fluid Mech. 629, 25–39.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C. M. 2010 Statistics of particle pair relative velocity in the homogeneous shear flow. Physica D 241, 245–250.CrossRefGoogle Scholar
Gualtieri, P., Picano, F., Sardina, G. & Casciola, C. M. 2013 Clustering and turbulence modulation in particle-laden shear flows. J. Fluid Mech. 715, 134–162.CrossRefGoogle Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016a The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects. J. Fluid Mech. 796, 617–658.CrossRefGoogle Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016b The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part II. Simulations with gravitational effects. J. Fluid Mech. 796, 659–711.CrossRefGoogle Scholar
Isaza, J. & Collins, L. R. 2009 On the asymptotic behaviour of large-scale turbulence in homogeneous shear flow. J. Fluid Mech. 637, 213–239.CrossRefGoogle Scholar
Iver, K. P., Sreenivasan, K. R. & Yeung, P. K. 2017 Reynolds number scaling of velocity increments in isotropic turbulence. Phys. Rev. E 95, 021101.Google Scholar
Johnson, P. L. & Meneveau, C. 2018 Predicting viscous-range velocity gradient dynamics in large-eddy simulation of turbulence. J. Fluid Mech. 837, 80–114.CrossRefGoogle Scholar
Jung, J., Yeo, K. & Lee, C. 2008 Behavior of heavy particles in isotropic turbulence. Phys. Rev. E 77, 016307.CrossRefGoogle ScholarPubMed
Kida, S. & Tanaka, M. 1994 Dynamics of vortical structures in a homogeneous shear flow. J. Fluid Mech. 274, 43–68.CrossRefGoogle Scholar
Kim, J. & Lim, J. 2000 A linear process in wall-bounded turbulent shear flows. Phys. Fluids 12 (8), 1885.CrossRefGoogle Scholar
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109–134.CrossRefGoogle Scholar
Lagaert, J. B., Balarac, G. & Cottet, G.-H. 2014 Hybrid spectral-particle method for the turbulent transport of a passive scalar. J. Comput. Phys. 260, 127–142.CrossRefGoogle Scholar
Lavezzo, V., Soldati, A., Gerashchenko, S., Warhaft, Z. & Collins, R. 2010 On the role of gravity and shear on inertial particle accelerations in near-wall turbulence. J. Fluid Mech. 658, 229–246.CrossRefGoogle Scholar
Lazero, B. J. & Lasheras, J. C. 1992 Particle dispersion in the developing free shear layer. J. Fluid Mech. 235, 143.CrossRefGoogle Scholar
Lee, C. M., Gylafson, A., Perlekar, P. & Toschi, F. 2015 Inertial particle acceleration in strained turbulence. J. Fluid Mech. 785, 31–53.CrossRefGoogle Scholar
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583.CrossRefGoogle Scholar
Longmire, E. K. & Eaton, J. K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217.CrossRefGoogle Scholar
Mamatsashvili, G., Khujadze, G., Chagelishvili, G., Dong, S., Jiménez, J. & Foysi, H. 2016 Dynamics of homogeneous shear turbulence: a key role of the nonlinear transverse cascade in the bypass concept. Phys. Rev. E 94, 023111.CrossRefGoogle ScholarPubMed
Martin, J. E. & Meiburg, E. 1994 The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. Phys. Fluids 6, 1116.CrossRefGoogle Scholar
Maxey, M. 1987 The gravitational settling of aerosol-particles in homogeneous turbulence and random flow-fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Minier, J.-P. 2015 On Lagrangian stochastic methods for turbulent polydispersed two-phase reactive flows. Prog. Energy Combust. Sci. 50, 1–62.CrossRefGoogle Scholar
Minier, J.-P. 2016 Statistical descriptions of polydisperse turbulent two-phase flows. Phys. Rep. 665, 1–122.CrossRefGoogle Scholar
Moffat, H. K. 1967 Interaction of turbulence with strong wind shear. In Atmosphere Turbulence and Radio Wave Propagation (ed. Yaglom, A. M. & Tatarsky, V. I.), pp. 139–156. Nauka.Google Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 11–133.CrossRefGoogle Scholar
Momenifar, M., Dhariwal, R. & Bragg, A. D. 2019 Influence of Reynolds number on the motion of settling, bidisperse inertial particles in turbulence. Phys. Rev. Fluids 4, 054301.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a voronoï analysis. Phys. Fluids 22, 113304.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 1–18.CrossRefGoogle Scholar
Monin, A. S. & Yaglom, A. M. 1981 Statistical Fluid Mechanics: Mechanics of Turbulence. MIT Press.Google Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 Three-dimensional structure of the Lagrangian acceleration in turbulent ows. Phys. Rev. Lett. 93 (21), 214501.CrossRefGoogle Scholar
Mordant, N., Deloura, J., Leveque, E., Arneodo, A. & Pinton, J.-F. 2002 Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence. Phys. Rev. Lett. 89, 254502.CrossRefGoogle ScholarPubMed
Mordant, N., Metz, P., Michel, O. & Pinton, J.-F. 2001 Measurement of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87, 214501.CrossRefGoogle ScholarPubMed
Mouri, H., Hori, A. & Kawashima, Y. 2002 Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the Reynolds number. Phys. Rev. E 67, 06305.Google Scholar
Nicolai, C., Jacob, B., Gualtieri, P. & Piva, R. 2014 Inertial particles in homogeneous shear turbulence: experiments and direct numerical simulation. Flow Turbul. Combust. 92, 65–82.CrossRefGoogle Scholar
Pope, S. B. 1990 Lagrangian microscales in turbulence. Phil. Trans. R. Soc. Lond. A 333, 309–319.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pope, S. B. 2004 Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35.CrossRefGoogle Scholar
Pumir, A. 1996 Turbulence in homogeneous shear flows. Phys. Fluids 8 (11), 3112–3127.CrossRefGoogle Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA Tech. Mem. 58B11.Google Scholar
Rogers, M. & Moin, P. 1987 The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66.CrossRefGoogle Scholar
Rouson, D. W. I. & Eaton, J. K. 2001 On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech. 428, 149–169.CrossRefGoogle Scholar
Sabelnikov, V., Barge, A. & Gorokhovski, M. A. 2019 Stochastic modeling of fluid acceleration on residual scales and dynamics of inertial particles suspended in turbulence. Phys. Rev. Fluids 4, 044301.CrossRefGoogle Scholar
Sabelnikov, V., Chtab-Desportes, A. & Gorokhovski, M. 2007 The coupled LES – subgrid stochastic acceleration model (LES-SSAM) of a high Reynolds number flows. In Advances in Turbulence XI, vol. 117, pp. 209–211. Springer Proceedings Physics.CrossRefGoogle Scholar
Sabel’nikov, V., Chtab-Desportes, A. & Gorokhovski, M. 2011 New sub-grid stochastic acceleration model in LES of high-Reynolds-number flows. Eur. Phys. J. B 80 (2), 177–187.CrossRefGoogle Scholar
Sagaut, P. 2001 Large Eddy Simulation for Incompressible Flows. Springer.CrossRefGoogle Scholar
Scotti, A. & Meneveau, C. 1999 A fractal model for large eddy simulation of turbulent flow. Physica D 127, 198–232.CrossRefGoogle Scholar
Sekimoto, A., Dong, S. & Jimenez, J. 2016 Direct numerical simulation of statistically stationary and homogeneous shear turbulence and its relation to other shear flows. Phys. Fluids 28, 035101.CrossRefGoogle Scholar
Shaw, R. 2003 Particle turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227.CrossRefGoogle Scholar
Shotorban, B. & Balachandar, S. 2006 Particle concentration in homogeneous shear turbulence simulated via Lagrangian and equilibrium Eulerian approaches. Phys. Fluids 18, 065105.CrossRefGoogle Scholar
Simonin, O. 1991 Prediction of the dispersed phase turbulence in particle-laden jets, gas-solid flows. ASME-FED 121, 197–206.Google Scholar
Simonin, O., Deutsch, E. & Boivin, M. 1993 Large eddy simulation and second-moment closure model of particle fluctuating motion in two-phase tubrulent shear flows. Turbul. Shear Flows 9, 85.Google Scholar
Stolz, S. & Adams, N. A. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 (7), 1699–1701.CrossRefGoogle Scholar
Tang, L., Wen, F., Crowe, T. C., Chung, J. N. & Troutt, T. R. 1991 Selforganizing particle dispersion mechanism in a plane wake. Phys. Fluids A 3, 130.Google Scholar
Tom, J. & Bragg, A. D. 2019 Multiscale preferential sweeping of particles settling in turbulence. J. Fluid Mech. 871, 244–270.CrossRefGoogle Scholar
Toschi, F., Amati, G., Succi, S., Benzi, R. & Piva, R. 1999 Intermittency and structure functions in channel flow turbulence. Phys. Rev. Lett. 82, 5044.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41 (1), 375–404.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wang, Y., Jacobitz, G. & Rutland, C. J. 2006 Large eddy simulation of homogeneous shear flows with several subgrid-scale models. Intl J. Numer. Meth. Fluids 50, 863–883.CrossRefGoogle Scholar
Yakhot, V. 2003 A simple model for self-sustained oscillations in homogeneous shear flow. Phys. Fluids 15 (2), L17.CrossRefGoogle Scholar
Yeh, F. & Lei, U. 1991 On the motion of small particles in a homogeneous turbulent shear flow. Phys. Fluids 3 (11), 2758.CrossRefGoogle Scholar
Yeung, P. K. 1997 One- and two-particle Lagrangian acceleration correlations in numerically simulated homogeneous turbulence. Phys. Fluids 9 (10), 2981–2990.CrossRefGoogle Scholar
Yeung, P. K., Sreenivasan, K. R. & Pope, S. B. 2018 Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence. Phys. Rev. Fluids 3, 064603.CrossRefGoogle Scholar
Yeung, P. K., Zhai, X. M. & Sreenivasan, K. R. 2015 Extreme events in computational turbulence. Proc. Natl Acad. Sci. 112 (41), 12633–12638.CrossRefGoogle ScholarPubMed
Zamansky, R., Vinkovic, I. & Gorokhovski, M. 2010 LES approach coupled with stochastic forcing of subgrid acceleration in a high-Reynolds number channel flow. J. Turbul. 11, 1–18.Google Scholar
Zamansky, R., Vinkovic, I. & Gorokhovski, M. 2011 Acceleration statistics of solid particles in turbulent channel flow. Phys. Fluids 23, 113304.CrossRefGoogle Scholar
Zamansky, R., Vinkovic, I. & Gorokhovski, M. 2013 Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application. J. Fluid Mech. 721, 627–668.CrossRefGoogle Scholar