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Wake–cylinder interactions of a hinged cylinder at low and intermediate Reynolds numbers

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Abstract

This paper is devoted to the study and classification of vortex-induced oscillation and the wake structure of flow past finite cylinders. Experiments were performed in a water tunnel using cylindrical particles hinged in the center of the test section while allowing them one degree of rotational freedom. The speed of flow and aspect ratio of the cylinders were used to vary the Reynolds number in the study between 100 and 5000. The cylinders display different responses to the fluid flow depending upon the Re, ranging from steady orientation, periodic oscillation to autorotation. A hydrogen bubble flow visualization technique was used to examine the vortex structure and supported by image analysis techniques. Specific features of the wake structure such as length of the primary vortex, its frequency and amplitude were analyzed as a function of Re. Our investigations indicate that the frequency of oscillation of the cylinder and the vortex shedding increases monotonically with the Reynolds number. Also, the length of the primary vortex versus Re shows interesting features and reveals possible critical points in the flow when vortex structure changes. In order to better understand qualitative aspects of the cylinder’s dynamics that go beyond experiments, a simplistic forced nonlinear pendulum toy model was employed and seen to capture qualitative aspects of the cylinder’s dynamics.

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Notes

  1. The characteristic length of the cylinder is taken to be its length (l).

  2. Cylinders of aspect ratio \(>\)1 oscillate around a different equilibrium from those with aspect ratio \(<\)1. If these aspect ratios were being considered in isolation, we would use the equilibrium configuration length to be equal to the characteristic length (i.e., for \(AR>1\), the characteristic length would be l, and for \(AR<1\), the characteristic length would equal the diameter d). However, since this current paper compares different aspect ratios, we feel it is meaningful to fix the characteristic length for all cylinders to be l.

  3. The bifurcation diagram , Fig. 5, only shows \(I^*\) up to a value of 0.5. For the case of \(I^*=0.62\), by extrapolation, we can expect the critical Reynolds number to lie close to 1500.

  4. Non-oscillation describes the critical behavior as the pendulum ascends to the maximum position and displays rotations with no reverse motion.

  5. This approximation at best delays the onset of critical phenomena, but otherwise does not change the physics of the problem being discussed here

  6. The non-dimensional time parameter in \(\alpha \) is computed by two means: a constant \(T_1=\frac{1}{\text {max}(\omega _0)}\) and also \(T_2=\frac{1}{\omega _0}\). In Table 2, we display only the second case of non-dimensionalization by \(T_2\).

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Acknowledgments

We acknowledge the help of several folks in this project. Among them, Greg Gipson, Danny Barry, Dr. Roberto Camassa, Dr. Eric Forgoston and Dr. Richard McLaughlin are acknowledged for their help and support. Part of this work was supported by the Science Honors Innovation Program (SHIP) at Montclair State University and by the National Science Foundation under Grant No. 1229113.

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Authors and Affiliations

  1. Complex Fluids Laboratory, Department of Mathematical Sciences, Montclair State University, Montclair, NJ, 07043, USA

    M. Cohrs, W. Ernst & A. Vaidya

  2. Department of Bioengineering, George Mason University, Fairfax, VA, 22030, USA

    B. Chung

  3. Department of Mechanical Engineering and Material Science, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    G. P. Galdi

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  1. B. Chung
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  2. M. Cohrs
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  3. W. Ernst
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  4. G. P. Galdi
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  5. A. Vaidya
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Correspondence to A. Vaidya.

Appendix: Parameter values chosen to solve Eq. (13)

Appendix: Parameter values chosen to solve Eq. (13)

See Table 2.

Table 2 This table presents a comparison of theoretical and experimental result in the estimation of frequency of oscillation of the cylinder as a function of the Reynolds number and cylinder’s aspect ratio
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Chung, B., Cohrs, M., Ernst, W. et al. Wake–cylinder interactions of a hinged cylinder at low and intermediate Reynolds numbers. Arch Appl Mech 86, 627–641 (2016). https://doi.org/10.1007/s00419-015-1051-2

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