Abstract

The Karman vortex street generated behind a circular cylinder in water flow field is displayed and analyzed in real time by means of digital holography. Using a modified Mach-Zehnder interferometer, a digital hologram of the flow field in still state and then a video of continuous digital holograms in flowing state are recorded at 14.6 frames per second by a CCD camera, respectively. A series of sequential phase maps of the flow field are numerically reconstructed from the holograms in different states above based on double-exposure holographic interferometry. By seriating these phase maps, the shape and evolution of Karman vortex street can be displayed in real time in the form of a movie. For comparison, numerical simulation of the Karman vortex street under the boundary conditions adopted in the experiment is also presented, and the consistent results indicate that the experimental observation of Karman vortex street by using digital holography is successful and feasible.

© 2009 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2009 (4)

2008 (4)

2007 (1)

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[CrossRef]

2006 (4)

2005 (2)

C. J. Mann, L. F. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13(22), 8693–8698 (2005).
[CrossRef] [PubMed]

J. L. Zhao, H. Q. Lu, X. S. Song, J. F. Li, and Y. H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249(4-6), 493–499 (2005).
[CrossRef]

2003 (2)

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[CrossRef] [PubMed]

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

2002 (1)

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14(4), 1340–1363 (2002).
[CrossRef]

2001 (4)

J. P. Crimaldi and J. R. Koseff, “High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume,” Exp. Fluids 31(1), 90–102 (2001).
[CrossRef]

C. Herman and E. Kang, “Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel,” Heat Mass Transfer. 37(1), 87–99 (2001).
[CrossRef]

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

L. Xu, X. Y. Peng, J. M. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40(28), 5046–5051 (2001).
[CrossRef]

2000 (1)

1998 (1)

G. Tanda and F. Devia, “Application of a schlieren technique to heat transfer measurements in free-convection,” Exp. Fluids 24(4), 285–290 (1998).
[CrossRef]

1992 (1)

P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows,” AIAA Pap. 1, 5–21 (1992).

1990 (1)

P. L. Bourget and D. Marichal, “Remarks about variations in the drag coefficient of circular cylinders moving through water,” Ocean Eng. 17(6), 569–585 (1990).
[CrossRef]

Allmaras, S. R.

P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows,” AIAA Pap. 1, 5–21 (1992).

Asundi, A. K.

Bert, J.

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[CrossRef]

Bourget, P. L.

P. L. Bourget and D. Marichal, “Remarks about variations in the drag coefficient of circular cylinders moving through water,” Ocean Eng. 17(6), 569–585 (1990).
[CrossRef]

Cannell, D. S.

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14(4), 1340–1363 (2002).
[CrossRef]

Charrière, F.

Colomb, T.

Colombani, J.

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[CrossRef]

Crimaldi, J. P.

J. P. Crimaldi and J. R. Koseff, “High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume,” Exp. Fluids 31(1), 90–102 (2001).
[CrossRef]

Cuche, E.

De Nicola, S.

Depeursinge, C.

Devia, F.

G. Tanda and F. Devia, “Application of a schlieren technique to heat transfer measurements in free-convection,” Exp. Fluids 24(4), 285–290 (1998).
[CrossRef]

Di, J. L.

Fan, Q.

Ferraro, P.

Finizio, A.

Garcia-Sucerquia, J.

Gorski, P.

P. Gorski, “Some aspects of the dynamic cross-wind response of tall industrial chimney,” Wind & Struct 12, 259–279 (2009).

Grilli, S.

Gusev, M. E.

Hennelly, B. M.

Herman, C.

C. Herman and E. Kang, “Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel,” Heat Mass Transfer. 37(1), 87–99 (2001).
[CrossRef]

Hossain, M. M.

M. M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48(10), 1869–1877 (2009).
[CrossRef] [PubMed]

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45(10), 106–203 (2006).
[CrossRef]

Javidi, B.

Jericho, M. H.

Jericho, S. K.

Jiang, H. Z.

Kang, E.

C. Herman and E. Kang, “Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel,” Heat Mass Transfer. 37(1), 87–99 (2001).
[CrossRef]

Katti, V.

V. Katti and S. V. Prabhu, “Heat transfer enhancement on a flat surface with axisymmetric detached ribs by normal impingement of circular air jet,” Int. J. Heat Fluid Flow 29(5), 1279–1294 (2008).
[CrossRef]

Kim, M. K.

Klages, P.

Koseff, J. R.

J. P. Crimaldi and J. R. Koseff, “High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume,” Exp. Fluids 31(1), 90–102 (2001).
[CrossRef]

Kreuzer, H. J.

Kuehn, J.

Li, E. P.

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

Li, J. F.

J. L. Zhao, H. Q. Lu, X. S. Song, J. F. Li, and Y. H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249(4-6), 493–499 (2005).
[CrossRef]

Lo, C. M.

Lu, H. Q.

J. L. Zhao, H. Q. Lu, X. S. Song, J. F. Li, and Y. H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249(4-6), 493–499 (2005).
[CrossRef]

Ma, Y. H.

J. L. Zhao, H. Q. Lu, X. S. Song, J. F. Li, and Y. H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249(4-6), 493–499 (2005).
[CrossRef]

Mann, C. J.

Marian, A.

Marichal, D.

P. L. Bourget and D. Marichal, “Remarks about variations in the drag coefficient of circular cylinders moving through water,” Ocean Eng. 17(6), 569–585 (1990).
[CrossRef]

Marquet, P.

McElhinney, C. P.

Mehta, D. S.

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45(10), 106–203 (2006).
[CrossRef]

Meng, H.

Meucci, R.

Miao, J. M.

Montfort, F.

Naughton, T. J.

Osten, W.

Pan, G.

Pedrini, G.

Peng, X. Y.

Pierattini, G.

Prabhu, S. V.

V. Katti and S. V. Prabhu, “Heat transfer enhancement on a flat surface with axisymmetric detached ribs by normal impingement of circular air jet,” Int. J. Heat Fluid Flow 29(5), 1279–1294 (2008).
[CrossRef]

Qin, C.

Shakher, C.

M. M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48(10), 1869–1877 (2009).
[CrossRef] [PubMed]

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45(10), 106–203 (2006).
[CrossRef]

Song, X. S.

J. L. Zhao, H. Q. Lu, X. S. Song, J. F. Li, and Y. H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249(4-6), 493–499 (2005).
[CrossRef]

Spalart, P. R.

P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows,” AIAA Pap. 1, 5–21 (1992).

Sun, W. W.

Tajahuerce, E.

Tanda, G.

G. Tanda and F. Devia, “Application of a schlieren technique to heat transfer measurements in free-convection,” Exp. Fluids 24(4), 285–290 (1998).
[CrossRef]

Trainoff, S. P.

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14(4), 1340–1363 (2002).
[CrossRef]

Wang, L.

Xu, L.

Xu, W. B.

Yang, D. S.

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

Yang, D. X.

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

Yang, S.

Yu, L. F.

Yu, Y. L.

Yuan, W. Z.

Zhang, P.

J. L. Di, J. L. Zhao, H. Z. Jiang, P. Zhang, Q. Fan, and W. W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47(30), 5654–5659 (2008).
[CrossRef] [PubMed]

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

Zhang, W.

Zhang, Y. C.

Zhao, J. L.

Zhou, J. B.

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

AIAA Pap. (1)

P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows,” AIAA Pap. 1, 5–21 (1992).

Appl. Opt. (9)

L. Xu, X. Y. Peng, J. M. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40(28), 5046–5051 (2001).
[CrossRef]

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[CrossRef] [PubMed]

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008).
[CrossRef] [PubMed]

J. L. Di, J. L. Zhao, H. Z. Jiang, P. Zhang, Q. Fan, and W. W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47(30), 5654–5659 (2008).
[CrossRef] [PubMed]

C. Qin, J. L. Zhao, J. L. Di, L. Wang, Y. L. Yu, and W. Z. Yuan, “Visually testing the dynamic character of a blazed-angle adjustable grating by digital holographic microscopy,” Appl. Opt. 48(5), 919–923 (2009).
[CrossRef] [PubMed]

M. M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48(10), 1869–1877 (2009).
[CrossRef] [PubMed]

Y. C. Zhang, J. L. Zhao, Q. Fan, W. Zhang, and S. Yang, “Improving the reconstruction quality with extension and apodization of the digital hologram,” Appl. Opt. 48(16), 3070–3074 (2009).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, W. B. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45(15), 3456–3462 (2006).
[CrossRef] [PubMed]

Chin. Phys. Lett. (1)

J. L. Zhao, P. Zhang, J. B. Zhou, D. X. Yang, D. S. Yang, and E. P. Li, “Visualizations of light-induced refractive index changes in photorefractive crystals employing digital holography,” Chin. Phys. Lett. 20(10), 1748–1751 (2003).
[CrossRef]

Exp. Fluids (2)

G. Tanda and F. Devia, “Application of a schlieren technique to heat transfer measurements in free-convection,” Exp. Fluids 24(4), 285–290 (1998).
[CrossRef]

J. P. Crimaldi and J. R. Koseff, “High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume,” Exp. Fluids 31(1), 90–102 (2001).
[CrossRef]

Heat Mass Transfer. (1)

C. Herman and E. Kang, “Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel,” Heat Mass Transfer. 37(1), 87–99 (2001).
[CrossRef]

Int. J. Heat Fluid Flow (1)

V. Katti and S. V. Prabhu, “Heat transfer enhancement on a flat surface with axisymmetric detached ribs by normal impingement of circular air jet,” Int. J. Heat Fluid Flow 29(5), 1279–1294 (2008).
[CrossRef]

J. Mol. Liq. (1)

J. Colombani and J. Bert, “Holographic interferometry for the study of liquids,” J. Mol. Liq. 134(1-3), 8–14 (2007).
[CrossRef]

Ocean Eng. (1)

P. L. Bourget and D. Marichal, “Remarks about variations in the drag coefficient of circular cylinders moving through water,” Ocean Eng. 17(6), 569–585 (1990).
[CrossRef]

Opt. Commun. (1)

J. L. Zhao, H. Q. Lu, X. S. Song, J. F. Li, and Y. H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249(4-6), 493–499 (2005).
[CrossRef]

Opt. Eng. (1)

M. M. Hossain, D. S. Mehta, and C. Shakher, “Refractive index determination: an application of lensless Fourier digital holography,” Opt. Eng. 45(10), 106–203 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Fluids (1)

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14(4), 1340–1363 (2002).
[CrossRef]

Wind & Struct (1)

P. Gorski, “Some aspects of the dynamic cross-wind response of tall industrial chimney,” Wind & Struct 12, 259–279 (2009).

Other (1)

T. Kreis, Handbook of Holographic Interferometry (WILEY-VCH GmbH and Co. KGaA, 2005).

Supplementary Material (2)

» Media 1: AVI (3800 KB)     
» Media 2: AVI (3741 KB)     

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for recording the digital hologram of the flow field in a rectangular channel. BS: beam splitter; M: mirror; TL: telecentric lens set; L: lens; MO: microscope objective; SF: pinhole; O : object wave; R : reference wave.

Fig. 2
Fig. 2

Schematic design of the sample for generating Karman vortex street. Inset: The planform of the measuring section. The blue arrow denotes the flow direction; the red arrow denotes the incident beam; the gray region denotes the circular cylinder; the two parallel lines respectively denote the right and left walls of the channel.

Fig. 3
Fig. 3

Digital holograms of the flow field in different states and their Fourier spectrum. (a) Hologram of the still flow field; (b) hologram of the flow field with velocity 2cm/s; (c) spatial spectra of the hologram in (a) and the rectangle filter window.

Fig. 4
Fig. 4

Reconstructed two-dimensional wrapped phase distributions of the Karman vortex street. (a)-(d) Four frames of the movie (Media 1) in a period.

Fig. 5
Fig. 5

Numerical simulation results of the Karman vortex street calculated by FLUENT (Media 2). The gray level represents the contour of vorticity magnitude.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

{uixi=0t(ρui)+xj(ρuiuj)=pxi+xj[μ(uixj+ujxi)]+xj(ρuiuj¯),
H(x,y)=|R(x,y)+O(x,y)|2        ​=[|O(x,y)|2+|R(x,y)|2]+R(x,y)O(x,y)+R(x,y)O(x,y),
Δφ(x,y)=arg[O1(x,y)O2(x,y)],
Δφ(x,y)=2πλΔl(x,y)=2πλ0L[n(x,y,z)n0]dz,

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