Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T09:35:16.183Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-Similar Analysis on Vortex Shedding Process

Published online by Cambridge University Press:  05 May 2011

C.-T. Wang  and
C.-T. Chen
C.-T. Wang*
Affiliation:
Dept. of Mechanical and Electro-Mechanical Engineering, National I Lan University, I Lan, Taiwan 26047, R.O.C.
C.-T. Chen*
Affiliation:
Dept. of Applied Mathematics, National University of Kaohsiung, Kaohsiung, Taiwan 81148, R.O.C.
*
*Assistant Professor
*Assistant Professor
Get access

Abstract

Chaos theory has been seen as an efficient tool for studying the turbulent flow, the findings of attractor were also important and made in the study to investigate the wake flow behind the bluff body. Here, the fractal dimension value would then be found by Hurst analysis. According to the results found, the Hurst empirical formula derived by the self-similar laceration of vortex plane would be applied by self-similar property to decide the band of the frequency variations in the vortex shedding process. The three kinds of flow mode with their individual attractors and characteristics could be decomposed and shown as following: self-similar laceration, energy input and white noise band. Finally, the energy ratio for the three kinds of flow mode had been confirmed. Hence, these findings would be helpful to further study the wake flow in the vortex shedding process.

Keywords

AttractorChaosHurst AnalysisWake Flow
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 4 , December 2006 , pp. 263 - 270
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Berger, E., “Periodic Flow Phenomena,” Annual Review of Fluid Mech., 4, p. 313 (1972).CrossRefGoogle Scholar
2.Okajima, A., “Strouhal Numbers of Rectangular Cylinders,” J. Fluid Mech. 123, p. 379 (1982).CrossRefGoogle Scholar
3.Huerre, P. and Monkewitz, P., “Local and Global Instabilities in Spatially Developing Flows,” Annual Review of Fluid Mech., 22, p. 473 (1990).CrossRefGoogle Scholar
4.Jackson, C. P., “A Finite-Element Study of the Onset of Vortex Shedding in Flow past Variously Shaped Bodies,” J.Fluid Mech., 182, p. 23 (1987).CrossRefGoogle Scholar
5.Kahawita, R. and Wang, P., “Numerical Simulation of the Wake Flow Behind Trapezoidal Bluff Bodies,” Computers & Fluids 31, p. 99 (2002).CrossRefGoogle Scholar
6.Miau, J. J., Wang, J. T., Chou, J. H. and Wei., C. Y., “Low-Frequency Fluctuations in the Near-Wake Region of a Trapezoidal Cylinder with Low Aspect Ratio,” Journal of Fluids and Structures, 17/5, p. 701 (2003).CrossRefGoogle Scholar
7.Townsend, A. A., “The Structures of Turbulent Shear Flows,” Cambridge Univ. Press (1976).Google Scholar
8.Corrsin, S. and Kistler, A L., “The Free-Stream Boundaries of Turbulent Flows,” NACATN3133 (1955).Google Scholar
9.Brown, F. N. M. and Roshko, A., “On Density Effects and Large Structure in Turbulent Mixing Layer,” J. FluidMech., 64, p. 775 (1974).CrossRefGoogle Scholar
10.Lorenz, E. N., “Deterministic Non-Periodic Flow,” J. Atmos. Sci., 20, p. 130(1963).2.0.CO;2>CrossRefGoogle Scholar
11.Mandelbrot, B. B., “Intermittent Turbulence and Fractal Dimension,” Turbulence and Navier-Stokes Equations, Temam, R., Ed., Lecture Notes in Mathematics 565, 121, Springer-Verlag (1976).CrossRefGoogle Scholar
12.Sreenivasan, K. R. and Meneveau, C., “The Fractal Facets of Turbulence,” J. Fluid Mech., 173, p. 355 (1986).CrossRefGoogle Scholar
13.Prasad, R. R. and Sreenivasan, K. R., “Quantitative Three-Dimensional Imaging and the Structure of Passive Scalar Fields in Fully Turbulent Flows,” J. Fluid Mech., 216, p. 1(1990).CrossRefGoogle Scholar
14.Lane-Serff, G. F., “Investigation of the Fractal Structure of Jets and Plumes,” J. Fluid Mech., 249, p. 521 (1993).CrossRefGoogle Scholar
15.Stolovitzky, G., Kailasnath, P. and Sreenivasan, K. R., “Refined Similarity Hypotheses for Passive Scalars Mixed by Turbulence,” J. Fluid Mech., 297, p. 275 (1995).CrossRefGoogle Scholar
16.Frederiksen, R. D., Dahm, W. J. A. and Dowling, D. R., “Experimental Assessment of Fractal Scale-Similarity in turbulent Flows, Part 1, One-Dimensional Intersections,” J. Fluid Mech., 327, p. 35 (1996).CrossRefGoogle Scholar
17.Frederiksen, R. D., Dahm, W. J. A. and Dowling, D. R., “Experimental Assessment of Fractal Scale Similarity in Turbulent Flows, Part 4, Effects of Reynolds and Schmidt Numbers,” J. Fluid Mech., 377, p. 169 (1998).CrossRefGoogle Scholar
18.Mandelbrot, B. B., Gaussian Self-Affinity and Fractals, Springer, New York (2002).Google Scholar
19.Lamperti, J. W., “Semi-Stable Processes,” Trans. Am. Math.Soc., 104, p. 62(1962).CrossRefGoogle Scholar
20.Feder, J., Fractals, Plenum Press, New York (1988).CrossRefGoogle Scholar
21.Telesca, L., Lapenna, V. and Macchiato, M., “Mono and Multi-Fractal Investigation of Scaling Properties in Temporal Patterns of Seismic Sequences,” Chaos, Solitons and Fractals, 19, p. 1(2004).CrossRefGoogle Scholar
22.Einstein, A., “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. 17, 549 (1905); Reprinted in Einstein’ Miraculous Year: Five Papers that Changed the Face of Physics, Stachel, J.., Princeton University Press, 1998).Google Scholar
23.Peters, E., Fractal Market Aalysis, John Wiley and Sons, Inc. USA (1994).Google Scholar
24.Richardson, L. F., Weather Prediction by Numerical Process, Cambridge Univ. Press (1922).Google Scholar
25.Mandelbrot, B. B., The Fractal Geometry of Nature, W. H. Freeman and Company, New York (1983).CrossRefGoogle Scholar
26.Liu, S.-D. and Liu, S.-K.Liu, ,Solitary Wave and Turbulence, Shanghai Scientific and Technological Education Publishing House, Shanghai, China (1994).Google Scholar
27.Sauer, T., Yorke, A. J. and Casdagli, M., “Embedology”, J. Stat. Phys., 65, p. 579 (1991).CrossRefGoogle Scholar
28.Fey, U., Konig, M. and Eckelmann, H., “A New Strouhal-Reynolds-Number Relationship for the Circular Cylinder in the Range of 47 < Re < 2 × 105”, Phys. Fluids, 10(7), p. 1547(1998).CrossRefGoogle Scholar
29.Whitney, H., “Differentiable Manifolds,” Ann. Math., 37, p. 645 (1926).CrossRefGoogle Scholar
30.Prigogine, Ilya, Introduction to Thermodynamics of Irreversible Processes, Wiley, John & Sons (1968).Google Scholar
31.Prigogine, Ilya, From Being to Becoming: Time and Complexity in the Physical Sciences, W. H. Freeman Company (1981).Google Scholar