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Instabilities of a freely moving spherical particle in a Newtonian fluid: Direct Numerical Simulation

  • Yuxiu Li ORCID logo EMAIL logo , Shashank S. Tiwari ORCID logo , Geoffrey M. Evans , Krishnaswamy Nandakumar and Jyeshtharaj B. Joshi ORCID logo
Published/Copyright: February 8, 2021
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International Journal of Chemical Reactor Engineering
From the journal International Journal of Chemical Reactor Engineering Volume 19 Issue 7

Abstract

Direct Numerical Simulations (DNS) were carried out for a freely falling/rising rigid particle in an otherwise quiescent fluid, using a non-Lagrangian multiplier based fictitious domain (FD) method. Validation studies showed that the proposed FD based DNS are in good agreement with the existing experimental results in the transition regime of falling/rising spheres. Simulations done in the transitional regime (50 < Reynolds number (Re) < 1800 and solid-to-fluid density ratios Γ=ρp/ρf from 0.08 to 4), confirmed that (i) a falling spherical particle (Γ = 4) exhibits a helical trajectory in the range 270 < Re < 320, and (ii) a rising particle (Γ = 0.5) shows a zig-zagging trajectory in the same range of Re. This finding closes the uncertainty to the question as to whether or not rising/falling particles exhibit a helical and a zig-zagging trajectory. In addition to this, a total of seven distinctive flow regimes were identified, which are as follows: (I) vertical straight path (II) steady oblique path (III) Wavy oblique path (IV) zig-zagging path (for 0.08 < Γ < 1) (V) helical path (for 1 < Γ < 4) (VI) early transition to chaos and (VII) chaotic regime. Regime IV occurs only for light particles (Γ < 1), whereas Regime V occurs only for heavy particles (Γ > 1). Fast Fourier Transform (FFT) analysis characterized the presence of a bimodal frequency similar to that exhibited by flow past an isolated stationary bluff body.

Keywords: Direct Numerical Simulation; flow instabilities; particle dynamics; vortex shedding
Corresponding authors: Geoffrey M. Evans, Department of Chemical Engineering, The University of Newcastle, Newcastle, Australia; Krishnaswamy Nandakumar, Department of Chemical Engineering, Louisiana State University, Baton Rouge, USA; and Jyeshtharaj B. Joshi, Department of Chemical Engineering, Institute of Chemical Technology, Nathalal Parekh Marg, Matunga (E), Mumbai, 400019, India, Homi Bhabha National Institute, Mumbai, India; and J. B. Joshi Research Foundation, Mumbai, India, E-mail: (G. M. Evans), (K. Nandakumar), and (J. B. Joshi)

Funding source: Natural Science Foundation of China

Award Identifier / Grant number: 51776043

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work was supported by Natural Science Foundation of China (51776043).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Achenbach, E. 1972. “Experiments on the Flow Past Spheres at Very High Reynolds Numbers.” Journal of Fluid Mechanics 54: 565–75, https://doi.org/10.1017/s0022112072000874.Search in Google Scholar

Achenbach, E. 1974. “Vortex Shedding from Spheres.” Journal of Fluid Mechanics 62: 209–21, https://doi.org/10.1017/s0022112074000644.Search in Google Scholar

Aljure, D. E., I. Rodríguez, O. Lehmkuhl, C. D. Pérez-Segarra, and A. Oliva. 2015. “Influence of Rotation on the Flow Over a Cylinder at Re=5000.” International Journal of Heat and Fluid Flow 55: 76–90, https://doi.org/10.1016/j.ijheatfluidflow.2015.07.015.Search in Google Scholar

Ayeni, O., S. S. Tiwari, C. Wu, J. B. Joshi, and N. Nandakumar. 2020. “Behavior of Particle Swarms at Low and Moderate Reynolds Numbers Using Computational Fluid Dynamics—Discrete Element Model.” Physics of Fluids 32: 073304, https://doi.org/10.1063/5.0008518.Search in Google Scholar

Bale, S., M. Sathe, O. Ayeni, A. S. Berrouk, J. B. Joshi, and K. Nandakumar. 2017. “Spatially Resolved Mass Transfer Coefficient for Moderate Reynolds Number Flows in Packed Beds: Wall Effects.” International Journal of Heat and Mass Transfer 110: 406–15, https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.052.Search in Google Scholar

Bale, S., S. Tiwari, M. Sathe, A. S. Berrouk, K. Nandakumar, and J. Joshi. 2018. “Direct Numerical Simulation Study of End Effects and D/d Ratio on Mass Transfer in Packed Beds.” International Journal of Heat and Mass Transfer 127: 234–44, https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.100.Search in Google Scholar

Bale, S., S. S. Tiwari, K. Nandakumar, and J. B. Joshi. 2019. “Effect of Schmidt Number and D/d Ratio on Mass Transfer through Gas-Solid and Liquid-Solid Packed Beds: Direct Numerical Simulations.” Powder Technology 354: 529–39, https://doi.org/10.1016/j.powtec.2019.05.067.Search in Google Scholar

Bluemink, J. J., D. Lohse, A. Prosperetti, and L. V. Wijngaarden. 2008. “A Sphere in a Uniformly Rotating or Shearing Flow.” Journal of Fluid Mechanics 600: 201–33, https://doi.org/10.1017/s0022112008000438.Search in Google Scholar

Brandon, D. J., and S. K. Aggarwal. 2001. “A Numerical Investigation of Particle Deposition on a Square Cylinder Placed in a Channel Flow.” Aerosol Science & Technology 34: 340–52, https://doi.org/10.1080/02786820121279.Search in Google Scholar

Brown, P. P., and D. F. Lawler. 2003. “Sphere Drag and Settling Velocity Revisited.” Journal of Environmental Engineering 129: 222–31.10.1061/(ASCE)0733-9372(2003)129:3(222)Search in Google Scholar

Deshpande, R., V. Kanti, A. Desai, and S. Mittal. 2017. “Intermittency of Laminar Separation Bubble on a Sphere During Drag Crisis.” Journal of Fluid Mechanics 812: 815–40, https://doi.org/10.1017/jfm.2016.827.Search in Google Scholar

Diaz-Goano, C., P. D. Minev, and K. Nandakumar. 2003. “A Fictitious Domain/finite Element Method for Particulate Flows.” Journal of Computational Physics 192: 105–23, https://doi.org/10.1016/s0021-9991(03)00349-8.Search in Google Scholar

Glowinski, R., T.-W. Pan, T. I. Hesla, and D. D. Joseph. 1999. “A Distributed Lagrange Multiplier/fictitious Domain Method for Particulate Flows.” International Journal of Multiphase Flow 25: 755–94, https://doi.org/10.1016/s0301-9322(98)00048-2.Search in Google Scholar

Hopf, E. 1948. “A Mathematical Example Displaying Features of Turbulence.” Communications on Pure and Applied Mathematics 1: 303–22, https://doi.org/10.1002/cpa.3160010401.Search in Google Scholar

Horowitz, M., and C. H. K. Williamson. 2010. “The Effect of Reynolds Number on the Dynamics and Wakes of Freely Rising and Falling Spheres.” Journal of Fluid Mechanics 651: 251–94, https://doi.org/10.1017/s0022112009993934.Search in Google Scholar

Jenny, M., J. Dušek, and G. Bouchet. 2004. “Instabilities and Transition of a Sphere Falling or Ascending Freely in a Newtonian Fluid.” Journal of Fluid Mechanics 508: 201–39, https://doi.org/10.1017/s0022112004009164.Search in Google Scholar

Johnson, T. A., and V. C. Patel. 1999. “Flow Past a Sphere up to a Reynolds Number of 300.” Journal of Fluid Mechanics 378: 19–70, https://doi.org/10.1017/s0022112098003206.Search in Google Scholar

Joshi, J. B., K. Nandakumar, A. W. Patwardhan, A. K. Nayak, V. Pareek, M. Gumulya, C. Wu, N. Minocha, E. Pal, M. Dhiman, V. Bhusare, S. Tiwari, D. Lote, C. Mali, A. Kulkarni, and S. Tamhankar. 2019. “Computational Fluid Dynamics.” In Advances of Computational Fluid Dynamics in Nuclear Reactor Design and Safety Assessment 21–238. Cambridge, United Kingdom: Woodhead Publishing.10.1016/B978-0-08-102337-2.00002-XSearch in Google Scholar

Kim, H. J., and P. A. Durbin. 1988. “Observations of the Frequencies in a Sphere Wake and of Drag Increase by Acoustic Excitation.” Physics of Fluids 31: 3260, https://doi.org/10.1063/1.866937.Search in Google Scholar

Lee, H., K. Hourigan, and M. C. Thompson. 2013. “Vortex-induced Vibration of a Neutrally Buoyant Tethered Sphere.” Journal of Fluid Mechanics 719: 97–128, https://doi.org/10.1017/jfm.2012.634.Search in Google Scholar

Magarvey, R. H., and R. L. Bishop. 1961. “Transition Ranges for Three-Dimnesional Wakes.” Canadian Journal of Physics 39: 1418–22, https://doi.org/10.1139/p61-169.Search in Google Scholar

Miau, J. J., J. T. Wang, J. H. Chou, and C. Y. Wei. 2003. “Low-frequency Fluctuations in the Near-Wake Region of a Trapezoidal Cylinder with Low Aspect Ratio.” Journal of Fluids and Structures 17: 701–15, https://doi.org/10.1016/s0889-9746(03)00007-0.Search in Google Scholar

Minev, P. D., and C. Ross Ethier. 1999. “A Characteristic/finite Element Algorithm for the 3-D Navier–Stokes Equations Using Unstructured Grids.” Computer Methods in Applied Mechanics and Engineering 178: 39–50, https://doi.org/10.1016/s0045-7825(99)00003-1.Search in Google Scholar

Mittal, R. 1999. “Planar Symmetry in the Unsteady Wake of a Sphere.” AIAA Journal 37: 388–90, https://doi.org/10.2514/3.14179.Search in Google Scholar

Mittal, R., J. J. Wilson, and F. M. Najjar. 2002. “Symmetry Properties of the Transitional Sphere Wake.” AIAA Journal 40: 579–82, https://doi.org/10.2514/2.1686.Search in Google Scholar

Reddy, R. K., J. B. Joshi, K. Nandakumar, and P. D. Minev. 2010b. “Direct Numerical Simulations of a Freely Falling Sphere Using Fictitious Domain Method: Breaking of Axisymmetric Wake.” Chemical Engineering Science 65: 2159–71, https://doi.org/10.1016/j.ces.2009.12.009.Search in Google Scholar

Reddy, R. K., M. J. Sathe, J. B. Joshi, K. Nandakumar, and G. M. Evans. 2013. “Recent Developments in Experimental (PIV) and Numerical (DNS) Investigation of Solid–Liquid Fluidized Beds.” Chemical Engineering Science 92: 1–12, https://doi.org/10.1016/j.ces.2012.11.017.Search in Google Scholar

Reddy, R. K., S. Jin, K. Nandakumar, P. D. Minev, and J. B. Joshi. 2010a. “Direct Numerical Simulation of Free Falling Sphere in Creeping Flow.” International Journal of Computational Fluid Dynamics 24: 109–20, https://doi.org/10.1080/10618562.2010.495320.Search in Google Scholar

Rodriguez, I., R. Borell, O. Lehmkuhl, C. D. P. Segarra, and A. Oliva. 2011. “Direct Numerical Simulation of the Flow over a Sphere at Re = 3700.” Journal of Fluid Mechanics 679: 263–87, https://doi.org/10.1017/jfm.2011.136.Search in Google Scholar

Sakamoto, H., and H. Haniu. 1990. “A Study on Vortex Shedding from Spheres in a Uniform Flow.” Journal of Fluids Engineering 112: 386–92, https://doi.org/10.1115/1.2909415.Search in Google Scholar

Sakamoto, H., and H. Haniu. 1995. “The Formation Mechanism and Shedding Frequency of Vortices from a Sphere in Uniform Shear Flow.” Journal of Fluid Mechanics 287: 151–71, https://doi.org/10.1017/s0022112095000905.Search in Google Scholar

Tiwari, S. S., E. Pal, S. Bale, N. Minocha, A. W. Patwardhan, K. Nandakumar, and J. B. Joshi. 2019b. “Flow Past a Single Stationary Sphere, 1. Experimental and Numerical Techniques.” Powder Technology 365: 115–48.10.1016/j.powtec.2019.01.037Search in Google Scholar

Tiwari, S. S., E. Pal, S. Bale, N. Minocha, A. W. Patwardhan, K. Nandakumar, and J. B. Joshi. 2019c. “Flow Past a Single Stationary Sphere, 2. Regime Mapping and Effect of External Disturbances.” Powder Technology 365: 215–43.10.1016/j.powtec.2019.04.032Search in Google Scholar

Tiwari, S. S., S. Bale, A. W. Patwardhan, K. Nandakumar, and J. B. Joshi. 2019a. “Insights into the Physics of Dominating Frequency Modes for Flow Past a Stationary Sphere: Direct Numerical Simulations.” Physics of Fluids 31: 045108, https://doi.org/10.1063/1.5083917.Search in Google Scholar

Tomboulides, A. G., and S. A. Orszag. 2000. “Numerical Investigation of Transitional and Weak Turbulent Flow Past a Sphere.” Journal of Fluid Mechanics 416: 45–73, https://doi.org/10.1017/s0022112000008880.Search in Google Scholar

Veeramani, C., P. D. Minev, and K. Nandakumar. 2007. “A Fictitious Domain Formulation for Flows with Rigid Particles: A Non-Lagrange Multiplier Version.” Journal of Computational Physics 224: 867–79, https://doi.org/10.1016/j.jcp.2006.10.028.Search in Google Scholar

Veldhuis, C. H. J., and A. Biesheuvel. 2007. “An Experimental Study of the Regimes of Motion of Spheres Falling or Ascending Freely in a Newtonian Fluid.” International Journal of Multiphase Flow 33: 1074–87, https://doi.org/10.1016/j.ijmultiphaseflow.2007.05.002.Search in Google Scholar

Williamson, C. H. K. 1996. “Vortex Dynamics in the Cylinder Wake.” Annual Review of Fluid Mechanics 28: 477–539, https://doi.org/10.1146/annurev.fl.28.010196.002401.Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/ijcre-2020-0151).

Received: 2020-08-29
Accepted: 2021-01-13
Published Online: 2021-02-08

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijcre-2020-0151
Keywords for this article
Direct Numerical Simulation; flow instabilities; particle dynamics; vortex shedding

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. 10.1515/ijcre-2021-0153
  4. Special Issue Articles
  5. Gas-liquid downward flow through narrow vertical conduits: effect of angle of entry and tube-diameter on flow patterns
  6. Liquid antisolvent recrystallization and solid dispersion of flufenamic acid with polyvinylpyrrolidone K-30
  7. Forced convection heat transfer study of a blunt-headed cylinder in non-Newtonian power-law fluids
  8. Comparative studies on the separation of endocrine disrupting compounds from aquatic environment by emulsion liquid membrane and hollow fiber supported liquid membrane
  9. Instabilities of a freely moving spherical particle in a Newtonian fluid: Direct Numerical Simulation
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