Investigación

 

Three-dimensional PIV measurements of bubble drag and lift coefficients in restricted media

 

J. Ortiz-Villafuerte*, W. D. Schmidl** and Y. A. Hassan**

 

* Departamento de Sistemas Nucleares, Instituto Nacional de Investigaciones Nucleares, Carretera México-Toluca s/n, La Marquesa, Ocoyoacac, Estado de México, MÉXICO 52750. e-mail: javier.ortiz@inin.gob.mx.

* Department of Nuclear Engineering, Texas A&M University, College Station, Texas, USA 77843-3133, e-mail: dschmidl@gmail.com; y-hassan@tamu.edu.

 

Received 24 May 2012
Accepted 23 May 2013

 

Abstract

A hybrid scheme combining Particle Image Velocimetry and Shadow Image Velocimetry has been used for a full-volume, three-dimensional, transient study of the shape, trajectory and forces acting on air bubbles rising in stagnant tap water in restricted media. The bubble Reynolds number ranged from 400 to 650. The three-dimensional reconstruction of the bubble was accomplished by combining images from two orthogonal views. This reconstruction process allowed for measurement of dimensions, orientation, trajectory, rotation, velocity and acceleration of an individual rising bubble. These parameters were then used to compute drag and lift forces acting on the bubble. Instantaneous values of drag and lift coefficients were then determined. These experimental results were compared to known experimental data and values obtained from correlations found in scientific literature. It was found that correlations intended for determining drag coefficient values should be adequately modified when necessary to account for wall impact, since the drag coefficient magnitude is considerably higher than that predicted by such correlations at Re below 550. Regarding the bubble lift coefficient, instantaneous data scatter noticeably as a function of Re, but average values agree within the range of known data.

The major contributors to the uncertainty in this experiment were the capability of accurately reconstructing the 2D shape of the bubbles from distorted and/or incomplete PIV images and determining the bubble centroid. An overall error of 7% was computed for the drag coefficient, but it rises up to 44% for the lift coefficient.

Keywords: PIV; bubble; lift; drag; coefficient.

 

PACS: 47.55.dd

 

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References

1. R. Clift, J.R. Grace, and M.E. Weber, Bubbles, Drops and Particles (Academic Press, New York, NY, 1978).         [ Links ]

2. L.S. Fan and K. Tsuchiya, Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions (Butterworth-Heinemann, Stoneham, MA, 1990).         [ Links ]

3. W.L. Haberman and R.K. Morton, An Experimental Investigation of the Drag and Shape of Air Bubbles Rising in Various Liquids (Report 802, NS 715-102, 1953).         [ Links ]

4. Z. Lanying, S. Balachandar, P. Fischer, and F. Najjar, J. Fluid Mech. 37 (2008) 271.         [ Links ]

5. E.E. Michaelides, J. Fluids Eng. 119 (1997) 233.         [ Links ]

6. F. Takemura, S. Takagi, J. Magnaudet, and Y. Matsumoto, J. Fluid Mech. 461 (2002) 277.         [ Links ]

7. C. Crowe, M. Sommerfeld, and Y. Tsuji, Multiphase Flows with Droplets and Particles (CRC Press, Boca Raton, FL, 1998).         [ Links ]

8. W.C. Park, J.F. Klausner, and R. Mei, Experiments in Fluids 19 (1995) 167.         [ Links ]

9. C.E. Brennen, Cavitation and Bubble Dynamics (Oxford University Press, New York, NY, 1995).         [ Links ]

10. J.R.C. Hunt, R.J. Perkins, and J.C.H. Fung, Review of the Problems of Modeling Disperse Two-Phase Flows. Multiphase Science and Technology. Volume 8 Two-Phase Flow Fundamentals. Editors G.F. Hewitt, J.H. Kim, R.T. Lahey, Jr., J.M. Delhaye, and N. Zuber, (Begell House, New York, NY, 1994) 595.         [ Links ]

11 . J. Magnaudet, M. Rivero, and J. Fabre, J. Fluid Mech. 284 (1995) 97.         [ Links ]

12. F. Takemura and J. Magnaudet, J. Fluid Mech. 461 (2003) 277.         [ Links ]

13. Y. Hardalupas, K. Hishida, M. Maeda, H. Morikita, A.M.K.P. Taylor, and J.H. Whitelaw, Applied Optics 33 (1994) 8147.         [ Links ]

14. S.M. Hwang, R. Kurose, F. Akamatsu, H. Tsuji, H. Makino, and M. Katsuki, Energy& Fuels 19 (2005) 382.         [ Links ]

15 . G.T. Marzan and H.M. Karara, Proc. of the Symposium on Close-Range Photogrammetric Systems (1975) 420.         [ Links ]

16. K. Okamoto, Y. A. Hassan, and W.D. Schmidl, Exp. Fluids 19 (1995) 342.         [ Links ]

17. Y.A. Hassan and O.G. Philip, Exp. Fluids23 (1997) 145.         [ Links ]

18. N. Ayache, Artificial Vision for Mobile Robots: Stereo Vision and MultisensoryPerception (The MIT Press, Cambridge, MA. 1991).         [ Links ]

19. J. Ortiz-Villafuerte, Y.A. Hassan, and W.D. Schmidl, Exp. Thermal Fluid Sci. 25 (2001) 43.         [ Links ]

20. J.R. Grace, T. Wairegi, and T. H. Nguyen, Trans. Inst. Chem. Eng. 54 (1976) 167.         [ Links ]

21. D. Bhaga and M.E. Weber, J. Fluid Mech. 105 (1981) 61.         [ Links ]

22. M.J. Pang and J.J. Wei, Nuclear Eng. Design 241 (2011) 2204.         [ Links ]

23. D.Z. Zhang and W.B. VanderHeyden, Int. J. Multiphase Flow 28 (2002) 805.         [ Links ]

24. A. Tomiyama, H. Tamai, I. Zun, and S. Hosokawa, Chem. Eng. Sci. 57 (2002) 1849.         [ Links ]

25. D. Legendre and J. Magnaudet, J. Fluid Mech. 368 (1998) 81.         [ Links ]