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Simulations of Asymmetric Flow Structures around a Moving Sphere at Moderate Reynolds Number

Published online by Cambridge University Press:  15 July 2015

D.-L. Young ,
C.-S. Wu ,
C. Wu  and
Y.-C. Lin
D.-L. Young
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
C.-S. Wu*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
C. Wu
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan
Y.-C. Lin
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan
*
*Corresponding author ([email protected])
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Abstract

The evolution of asymmetric leeward-side flow structures around a moving sphere in the viscous flow is investigated. Simulations are carried out to investigate the variations of vortex-ring system at the moderate Reynolds number. A parallel laboratory experiment is undertaken in this study. The sphere travels a certain distance at constant speed and then stops to collide with a wall. The motion of moving sphere in fluid is described by the hybrid Cartesian immersed boundary method. Drag forces behind the moving sphere are extremely substantial as the solid body falls through viscous fluid for comprehending the formation of wake flow. The dynamic behavior consists of growth and breakup of the vortices which depend on two specific moderate Reynolds numbers. The onset of physical instability in the wake is obviously affected at the Reynolds number of 800. The generated vortex-ring system rolls upward to compact the primary vortex ring and interact with the secondary vortex. An asymmetric generation of the pairs of vortices is developed since the physical instability effect leads to shed in the wake with the increasing Reynolds number. The results from numerical simulations are also conducted to exhibit good comparison with those from the laboratory experiment.

Keywords

Moving sphereImmersed boundary methodModerate Reynolds numberVortex ring
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 6 , December 2015 , pp. 757 - 769
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

REFERENCES

1.Tompson, M. C., Leweke, T. and Hourigan, K., “Sphere-Wall Collisions: Vortex Dynamics and Stability,” Journal of Fluid Mechanics, 575, pp. 121–148 (2007).CrossRefGoogle Scholar
2.Leweke, T., Tompson, M. C. and Hourigan, K., “Vortex Dynamics Associated with the Collision of a Sphere with a Wall,” Physics of Fluids, 16, pp. 74–77 (2004).Google Scholar
3.Ye, T., Mittal, R., Udaykumar, H. S. and Shyy, W., “An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries,” Journal of Computational Physics, 156, pp. 209–240 (1999).Google Scholar
4.Udaykumar, H. S., Mittal, R., Rampunggoon, P. and Khanna, A., “A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries,” Journal of Computational Physics, 174, pp. 345–380 (2001).Google Scholar
5.Tucker, P. G. and Pan, Z., “A Cartesian Cut Cell Method for Incompressible Viscous Flow,” Applied Mathematical Modeling, 24, pp. 591–606 (2000).Google Scholar
6.Perskin, C. S., “Flow Pattern Around Heart Valves: A Numerical Method,” Journal of Computational Physics, 10, pp. 252–271 (1972).Google Scholar
7.Perskin, C. S., “Numerical Analysis of Blood Flow in The Heart,” Journal of Computational Physics, 25, pp. 220–252 (1977).Google Scholar
8.Lai, M. C. and Perskin, C. S., “An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity,” Journal of Computational Physics, 160, pp. 705–719 (2000).Google Scholar
9.Goldstein, D., Handler, R. and Sirovich, L., “Modeling a No-Slip Flow Boundary with an External Force Field,” Journal of Computational Physics, 105, pp. 354–366 (1993).Google Scholar
10.Saiki, E. M. and Birinsen, S., “Numerical Simulation of a Cylinder in Uniform Flow: Application of a Virtual Boundary Method,” Journal of Computational Physics, 123, pp. 450–465 (1996).Google Scholar
11.Mohd-Yusof, J., “Combined Immersed-Boundary/B-Splines Method for Simulations of Flow in Complex Geometries,” CTR Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University (1997).Google Scholar
12.Fadlun, E. A., Verzicco, R., Orlandi, P. and Mohd-Yusof, J., “Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations,” Journal of Computational Physics, 207, pp. 35–60 (2000).Google Scholar
13.Gilmanov, A. and Sotiropoulos, F., “A Hybrid Cartesian/Immersed Boundary Method for Simulating Flow with 3D, Geometrically Complex, Moving Boundary,” Journal of Computational Physics, 207, pp. 457–492 (2005).Google Scholar
14.Marella, S., Krishnan, S., Liu, H. and Udaykumar, H. S., “Sharp Interface Cartesian Grid Method I: An Easily Implemented Technique for 3D Moving Boundary Computations,” Journal of Computational Physics, 210, pp. 1–31 (2005).Google Scholar
15.Young, D. L., Chiu, C. L. and Fan, C. M., “A Hybrid Cartesian/Immersed-Boundary Finite-Element Method for Simulating Heat and Flow Patterns in a Two-Roll Mill,” Numerical Heat Transfer Part B-Fundamentals, 51, pp. 251–274 (2007).Google Scholar
16.Chorin, A. J., “Numerical Solution of the Navier-Stokes Equations,” Mathematics of Computation, 22, pp. 745–762 (1968).Google Scholar
17.Temam, R., “Une Méthod Dápproximation De La Solution Des Équations De Navier-Stokes,” Bulletin De La Société Mathématique De France, 98, pp. 115–152 (1968).Google Scholar
18.Wu, C. S. and Young, D. L., “Simulation of Wave-Structure Interaction Problem by a Strong Coupling Partitioned Approach,” Computers & Fluids, 89, pp. 66–77 (2014).Google Scholar
19.Eames, I. and Dalziel, S. B., “Dust Resuspension by the Flow Around an Impacting Sphere,” Journal of Fluid Mechanics, 403, pp. 305–328 (2000).Google Scholar
20.Tomboulides, A. G. and Orszag, S. A., “Numerical Investigation of Transitional and Weak Turbulent Flow Past a Sphere,” Journal of Fluid Mechanics, 416, pp. 45–73 (2000).Google Scholar
21.Johnson, T. A. and Patel, V. C., “Flow Past a Sphere Up to a Reynolds Number of 300,” Journal of Fluid Mechanics, 378, pp. 19–70 (1999).Google Scholar
22.Ormières, D. and Provansal, M., “Transition to Turbulence in the Wake of a Sphere,” Physical Review Letters, 83, pp. 80–83 (1999).Google Scholar