Hostname: page-component-669899f699-7tmb6 Total loading time: 0 Render date: 2025-04-26T01:46:01.766Z Has data issue: false hasContentIssue false
  • English
  • Français

Decay rate of homogeneous isotropic turbulence laden with finite-size particles

Published online by Cambridge University Press:  13 September 2024

Qichao Sun ,
Cheng Peng Open the ORCID record for Cheng Peng [Opens in a new window] ,
Lian-Ping Wang Open the ORCID record for Lian-Ping Wang [Opens in a new window] ,
Songying Chen  and
Zuchao Zhu
Qichao Sun
Affiliation:
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, PR China
Cheng Peng*
Affiliation:
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, PR China
Lian-Ping Wang
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, PR China
Songying Chen
Affiliation:
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, PR China
Zuchao Zhu
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, PR China
*
†Email address for correspondence: pengcheng@sdu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

This study conducts particle-resolved direct numerical simulations to analyse how finite-size spherical particles affect the decay rate of turbulent kinetic energy in non-sustained homogeneous isotropic turbulence. The decaying particle-laden homogeneous isotropic turbulence is generated with two set-ups, i.e. (1) releasing particles into a single-phase decaying homogeneous isotropic turbulence and (2) switching off the driving force of a sustained particle-laden homogeneous isotropic turbulence. With both set-ups, the decay of turbulent kinetic energy follows a power-law when the flow is fully relaxed, similar to their single-phase counterparts. The dependence of the power-law decay exponent $n$ on the particle-to-fluid density ratio, particle size and volume fraction is also investigated, and a predictive model is developed. We find that the presence of heavier particles slows down the long-time power-law decay exponent.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 993 , 25 August 2024 , A15
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abdelsamie, A.H. & Lee, C. 2012 Decaying versus stationary turbulence in particle-laden isotropic turbulence: turbulence modulation mechanism. Phys. Fluids 24 (1), 015106.CrossRefGoogle Scholar
Anas, M., Joshi, P. & Verma, M.K. 2020 Freely decaying turbulence in a finite domain at finite Reynolds number. Phys. Fluids 32 (9), 095109.CrossRefGoogle Scholar
Balachandar, S. 2009 A scaling analysis for point–particle approaches to turbulent multiphase flows. Intl J. Multiphase Flow 35 (9), 801–810.CrossRefGoogle Scholar
Batchelor, G.K. 1948 Energy decay and self-preserving correlation functions in isotropic turbulence. Q. Appl. Maths 6 (2), 97–116.CrossRefGoogle Scholar
Brändle de Motta, J.C., Breugem, W.-P., Gazanion, B., Estivalezes, J.-L., Vincent, S. & Climent, E. 2013 Numerical modelling of finite-size particle collisions in a viscous fluid. Phys. Fluids 25 (8), 083302.CrossRefGoogle Scholar
Brändle de Motta, J.C., Estivalezes, J.-L., Climent, E. & Vincent, S. 2016 Local dissipation properties and collision dynamics in a sustained homogeneous turbulent suspension composed of finite size particles. Intl J. Multiphase Flow 85, 369–379.CrossRefGoogle Scholar
Brändle de Motta, J.C., et al. 2019 Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows. Comput. Fluids 179, 1–14.CrossRefGoogle Scholar
Burton, T.M. & Eaton, J.K. 2005 Fully resolved simulations of particle-turbulence interaction. J. Fluid Mech. 545, 67–111.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25 (4), 657–682.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 48 (2), 273–337.CrossRefGoogle Scholar
Crowe, C.T., Schwarzkopf, J.D., Sommerfeld, M. & Tsuji, Y. 2011 Multiphase Flows with Droplets and Particles. CRC Press.CrossRefGoogle Scholar
Djenidi, L., Kamruzzaman, M. & Antonia, R.A. 2015 Power-law exponent in the transition period of decay in grid turbulence. J. Fluid Mech. 779, 544–555.CrossRefGoogle Scholar
Eaton, J.K. 2009 Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking. Intl J. Multiphase Flow 35 (9), 792–800.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G.C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modification. Phys. Fluids A 5 (7), 1790–1801.CrossRefGoogle Scholar
Elgobashi, S. 2006 An updated classification map of particle-laden turbulent flows. Proc. IUTAM Symp. Comput. Multiphase Flow 1, 3–10.Google Scholar
Eswaran, V. & Pope, S.B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16 (3), 257–278.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315–329.CrossRefGoogle Scholar
Gao, H., Li, H. & Wang, L.-P. 2013 Lattice Boltzmann simulation of turbulent flow laden with finite-size particles. Comput. Maths Applics. 65 (2), 194–210.CrossRefGoogle Scholar
George, W.K. 1992 The decay of homogeneous isotropic turbulence. Phys. Fluids A 4 (7), 1492–1509.CrossRefGoogle Scholar
George, W.K. 2013 Lectures in Turbulence for the 21st Century. Chalmers University of Technology 550.Google Scholar
George, W.K. & Wang, H. 2009 The exponential decay of homogeneous turbulence. Phys. Fluids 21 (2), 025108.CrossRefGoogle Scholar
Gore, R.A. & Crowe, C.T. 1989 Effect of particle size on modulating turbulent intensity. Intl J. Multiphase Flow 15 (2), 279–285.CrossRefGoogle Scholar
Huang, M.-J. & Leonard, A. 1994 Power-law decay of homogeneous turbulence at low Reynolds numbers. Phys. Fluids 6 (11), 3765–3775.CrossRefGoogle Scholar
Hurst, D. & Vassilicos, J.C. 2007 Scalings and decay of fractal-generated turbulence. Phys. Fluids 19 (3), 035103.CrossRefGoogle Scholar
Kidanemariam, A.G., Chan-Braun, C., Doychev, T. & Uhlmann, M. 2013 Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys. 15 (2), 025031.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 On degeneration (decay) of isotropic turbulence in an incompressible viscous liquid. Dokl. Akad. Nauk SSSR 31, 538–540.Google Scholar
Krogstad, P.-Å. & Davidson, P.A. 2010 Is grid turbulence Saffman turbulence? J. Fluid Mech. 642, 373–394.CrossRefGoogle Scholar
Lin, C.C. 1948 Note on the law of decay of isotropic turbulence. Proc. Natl Acad. Sci. USA 34 (11), 540–543.CrossRefGoogle ScholarPubMed
Ling, Y., Parmar, M. & Balachandar, S. 2013 A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Intl J. Multiphase Flow 57, 102–114.CrossRefGoogle Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5–55.CrossRefGoogle Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2011 Is stokes number an appropriate indicator for turbulence modulation by particles of Taylor-length-scale size? Phys. Fluids 23 (2), 025101.CrossRefGoogle Scholar
Luo, K., Wang, Z., Li, D., Tan, J. & Fan, J. 2017 Fully resolved simulations of turbulence modulation by high-inertia particles in an isotropic turbulent flow. Phys. Fluids 29 (11), 113301.CrossRefGoogle Scholar
Mansour, N.N. & Wray, A.A. 1994 Decay of isotropic turbulence at low Reynolds number. Phys. Fluids 6 (2), 808–814.CrossRefGoogle Scholar
Mohamed, M.S. & Larue, J.C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.CrossRefGoogle Scholar
Naso, A. & Prosperetti, A. 2010 The interaction between a solid particle and a turbulent flow. New J. Phys. 12 (3), 033040.CrossRefGoogle Scholar
Oka, S. & Goto, S. 2022 Attenuation of turbulence in a periodic cube by finite-size spherical solid particles. J. Fluid Mech. 949, A45.CrossRefGoogle Scholar
Peng, C. 2018 Study of turbulence modulation by finite-size solid particles with the lattice Boltzmann method. PhD thesis, University of Delaware.Google Scholar
Peng, C., Ayala, O.M., Brändle de Motta, J.C. & Wang, L.-P. 2019 A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method. Part 2. Turbulent flows. Comput. Fluids 192, 104251.CrossRefGoogle Scholar
Peng, C., Sun, Q. & Wang, L.-P. 2023 Parameterization of turbulence modulation by finite-size solid particles in forced homogeneous isotropic turbulence. J. Fluid Mech. 963, A6.CrossRefGoogle Scholar
Righetti, M. & Romano, G.P. 2004 Particle–fluid interactions in a plane near-wall turbulent flow. J. Fluid Mech. 505, 93–121.CrossRefGoogle Scholar
Saffman, P.G. 1967 Note on decay of homogeneous turbulence. Phys. Fluids 10 (6), 1349–1349.CrossRefGoogle Scholar
Schneiders, L., Meinke, M. & Schröder, W. 2017 Direct particle–fluid simulation of Kolmogorov-length-scale size particles in decaying isotropic turbulence. J. Fluid Mech. 819, 188–227.CrossRefGoogle Scholar
Seoud, R.E. & Vassilicos, J.C. 2007 Dissipation and decay of fractal-generated turbulence. Phys. Fluids 19 (10), 105108.CrossRefGoogle Scholar
Shen, J., Peng, C., Wu, J., Chong, K.L., Lu, Z. & Wang, L.-P. 2022 Turbulence modulation by finite-size particles of different diameters and particle–fluid density ratios in homogeneous isotropic turbulence. J. Turbul. 23 (8), 433–453.CrossRefGoogle Scholar
Sinhuber, M., Bodenschatz, E. & Bewley, G.P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114 (3), 034501.CrossRefGoogle ScholarPubMed
Tanaka, T. & Eaton, J.K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101 (11), 114502.CrossRefGoogle ScholarPubMed
Wang, L.-P., Ardila, O.G.C., Ayala, O., Gao, H. & Peng, C. 2016 Study of local turbulence profiles relative to the particle surface in particle-laden turbulent flows. J. Fluids Engng 138 (4), 041307.CrossRefGoogle Scholar
Yoffe, S.R. & McComb, W.D. 2018 Onset criteria for freely decaying isotropic turbulence. Phys. Rev. Fluids 3 (10), 104605.CrossRefGoogle Scholar
Yu, H., Girimaji, S.S. & Luo, L.-S. 2005 Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence. Phys. Rev. E 71 (1), 016708.CrossRefGoogle ScholarPubMed
Yu, Z., Xia, Y., Guo, Y. & Lin, J. 2021 Modulation of turbulence intensity by heavy finite-size particles in upward channel flow. J. Fluid Mech. 913, A3.CrossRefGoogle Scholar
Supplementary material: File

Sun et al. supplementary material

Sun et al. supplementary material
Download Sun et al. supplementary material(File)
File 49 KB