Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Aidun, C. K. , Lu, Y. , and Ding, E. J. , “Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation,” J. Fluid Mech. 373, 287311 (1998).
Andersen, A. , Pesavento, U. , and Wang, Z. J. , “Analysis of transitions between fluttering, tumbling and steady descent of falling cards,” J. Fluid Mech. 541, 91104 (2005a).
Andersen, A. , Pesavento, U. , and Wang, Z. J. , “Unsteady aerodynamics of fluttering and tumbling plates,” J. Fluid Mech. 541, 6590 (2005b).
Assemat, P. , Fabre, D. , and Magnaudet, J. , “The onset of unsteadiness of two-dimensional bodies falling or rising in a viscous fluid: A linear study,” J. Fluid Mech. 690, 173202 (2012).
Auguste, F. , Magnaudet, J. , and Fabre, D. , “Falling styles of disks,” J. Fluid Mech. 719, 388405 (2013).
Belmonte, A. , Eisenberg, H. , and Moses, E. , “From flutter to tumble: Inertial drag and froude similarity in falling paper,” Phys. Rev. Lett. 81(2), 345348 (1998).
Bonisch, S. and Heuveline, V. , “On the numerical simulation of the unsteady free fall of a solid in fluid. I. The Newtonian case,” Comput. Fluids 36(9), 14341445 (2007).
Chrust, M. , Bouchet, G. , and Dušek, J. , “Numerical simulation of the dynamics of freely falling discs,” Phys. Fluids 25(4), 044102 (2013).
Ern, P. , Risso, F. , Fabre, D. , and Magnaudet, J. , “Wake-induced oscillatory paths of bodies freely rising or falling in fluids,” Annu. Rev. Fluid Mech. 44(44), 97121 (2012).–101250
Feng, J. , Hu, H. H. , and Joseph, D. D. , “Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 1. Sedimentation,” J. Fluid Mech. 261, 95134 (1994a).
Feng, J. , Hu, H. H. , and Joseph, D. D. , “Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows,” J. Fluid Mech. 277, 271301 (1994b).
Field, S. B. , Klaus, M. , Moore, M. G. , and Nori, F. , “Chaotic dynamics of falling disks,” Nature 388(6639), 252254 (1997).
Gazzola, M. , Chatelain, P. , Rees, W. M. V. , and Koumoutsakos, P. , “Simulations of single and multiple swimmers with non-divergence free deforming geometries,” J. Comput. Phys. 230, 70937114 (2011).
Huang, H. , Yang, X. , and Lu, X. Y. , “Sedimentation of an ellipsoidal particle in narrow tubes,” Phys. Fluids 26(5), 053302 (2014).
Isaacs, J. L. and Thodos, G. , “The free-settling of solid cylindrical particles in the turbulent regime,” Can. J. Chem. Eng. 45(3), 150155 (1967).
Iversen, J. D. , “Autorotation flate-plate wings: The effect of the moment of inertia, geometry and Reynolds number,” J. Fluid Mech. 92, 327348 (1979).
Jin, C. and Xu, K. , “A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation,” J. Comput. Phys. 222(1), 155175 (2007).
Jones, M. A. and Shelley, M. J. , “Falling cards,” J. Fluid Mech. 540, 393425 (2005).
Lee, C. B. , Su, Z. , Zhong, H. J. , Chen, S. Y. , Zhou, M. D. , and Wu, J. Z. , “Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral,” J. Fluid Mech. 732, 77104 (2013).
Maxwell, J. C. , Niven, W. D. , and Maxwell, J. C. , On a Particular Case of the Descent of a Heavy Body in a Resisting Medium (Cambridge University Press, 1853).
Mittal, R. , Seshadri, V. , and Udaykumar, H. S. , “Flutter, tumble and vortex induced autorotation,” Theor. Comput. Fluid Dyn. 17(3), 165170 (2004).
Pesavento, U. and Wang, Z. J. , “Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation,” Phys. Rev. Lett. 93(14), 144501 (2004).
Shu, C. , Wang, Y. , Teo, C. J. , and Wu, J. , “Development of lattice Boltzmann flux solver for simulation of incompressible flows,” Adv. Appl. Math. Mech. 6, 436460 (2014).
Smith, E. H. , “Autorotating wings: An experimental investigation,” J. Fluid Mech. 50, 513534 (1971).
Tian, F. B. , Dai, H. , Luo, H. , Doyle, J. F. , and Rousseau, B. , “Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems,” J. Comput. Phys. 258, 451469 (2014).
Vincent, L. , Shambaugh, W. S. , and Kanso, E. , “Holes stabilize freely falling coins,” J. Fluid Mech. 801, 250259 (2016).
Wang, Y. , Shu, C. , Teo, C. J. , and Wu, J. , “An immersed boundary-lattice Boltzmann flux solver and its applications to flow-structure interaction problems,” J. Fluids Struct. 54, 440465 (2015).
Wang, Z. J. , “Dissecting insect flight,” Annual Rev. Fluid Mech. 37, 183210 (2005).
Wu, J. , Chen, Y. L. , and Zhao, N. , “Role of induced vortex interaction in a semi-active foil based energy harvester,” Phys. Fluids 27, 093601 (2015).
Zhong, H. , Chen, S. Y. , and Lee, C. , “Experimental study of freely falling thin disks: Transition from planar zigzag to spiral,” Phys. Fluids 23, 011702 (2011).
Zhong, H. J. , Lee, C. B. , Su, Z. , Chen, S. Y. , Zhou, M. D. , and Wu, J. Z. , “Experimental investigation of freely falling thin disks. I. The flow structures and Reynolds number effects on the zigzag motion,” J. Fluid Mech. 716, 228250 (2013).

Data & Media loading...


Article metrics loading...



A numerical study on two-dimensional (2D) rectangular plates falling freely in water is carried out in the range of 1.2 ≤ ≤ 5.0 and 1/20 ≤ ≤ 1/4, where is the solid-to-water density ratio and is the plate thickness-to-length ratio. To study this problem, the immersed boundary-lattice Boltzmann flux solver in a moving frame is applied and validated. For the numerical result, a phase diagram is constructed for fluttering, tumbling, and apparent chaotic motions of the plate parameterized using and . The evolution of vortical structures in both modes is decomposed into three typical stages of initial transient, deep gliding, and pitching-up. Various mean and instantaneous fluid properties are illustrated and analyzed. It is found that fluttering frequencies have a linear relationship with the Froude number for all cases considered. Lift forces on fluttering plates are linearly dependent on the angle of attack at the cusp-like turning point when . Hysteresis of the lift force on fluttering plates is observed and explained whilst the drag forces are the same when has the same value. Meanwhile, the drag force in the tumbling motion may have a positive propulsive effect when the plate begins a tumbling rotation from = /2.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd