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Geometry of unsteady fluid transport during fluid–structure interactions

Published online by Cambridge University Press:  08 October 2007

ELISA FRANCO ,
DAVID N. PEKAREK ,
JIFENG PENG  and
JOHN O. DABIRI
ELISA FRANCO
Affiliation:
Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA
DAVID N. PEKAREK
Affiliation:
Mechanical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
JIFENG PENG
Affiliation:
Bioengineering, California Institute Of Technology, Pasadena, CA 91125, USA
JOHN O. DABIRI
Affiliation:
Bioengineering, California Institute Of Technology, Pasadena, CA 91125, USA Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, [email protected]
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Abstract

We describe the application of tools from dynamical systems to define and quantify the unsteady fluid transport that occurs during fluid–structure interactions and in unsteady recirculating flows. The properties of Lagrangian coherent structures (LCS) are used to enable analysis of flows with arbitrary time-dependence, thereby extending previous analytical results for steady and time-periodic flows. The LCS kinematics are used to formulate a unique, physically motivated definition for fluid exchange surfaces and transport lobes in the flow. The methods are applied to numerical simulations of two-dimensional flow past a circular cylinder at a Reynolds number of 200; and to measurements of a freely swimming organism, the Aurelia aurita jellyfish. The former flow provides a canonical system in which to compare the present geometrical analysis with classical, Eulerian (e.g. vortex shedding) perspectives of fluid–structure interactions. The latter flow is used to deduce the physical coupling that exists between mass and momentum transport during self-propulsion. In both cases, the present methods reveal a well-defined, unsteady recirculation zone that is not apparent in the corresponding velocity or vorticity fields. Transport rates between the ambient flow and the recirculation zone are computed for both flows. Comparison of fluid transport geometry for the cylinder crossflow and the self-propelled swimmer within the context of existing theory for two-dimensional lobe dynamics enables qualitative localization of flow three-dimensionality based on the planar measurements. Benefits and limitations of the implemented methods are discussed, and some potential applications for flow control, unsteady propulsion, and biological fluid dynamics are proposed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 589 , 25 October 2007 , pp. 125 - 145
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.CrossRefGoogle Scholar
Dabiri, J. O., Colin, S. P., Costello, J. H., Gharib, M. 2005 Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses. J. Expl Biol. 208, 1257–1265.CrossRefGoogle ScholarPubMed
Duan, J. & Wiggins, S. 1997 Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics. Nonlinear Proc. Geophys. 4, 125–136.CrossRefGoogle Scholar
Fatouraee, N. & Amini, A. A. 2003 Regularization of flow streamlines in multislice phase-contrast MR imaging. IEEE Trans. Medical Imaging 22, 699–709.CrossRefGoogle ScholarPubMed
Green, M., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111–120.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. J. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.CrossRefGoogle Scholar
Haller, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147, 352–370.Google Scholar
Haller, G. 2001 Lagrangian structures and the rate of strain in a partition of two-dimensional turbulences. Phys. Fluids 13, 3368–3385.Google Scholar
Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14, 1851–1861.CrossRefGoogle Scholar
Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 1–26.CrossRefGoogle Scholar
Krueger, P. S. 2006 Measurement of propulsive power and evaluation of propulsive performance from the wake of a self-propelled vehicle. Bioinsp. Biomim. 1, S49–S56.Google Scholar
Malhotra, N. & Wiggins, S. 1998 Geometric structures, lobe dynamics, and lagrangian transport in flows with aperiodic time-dependence with applications to Rossby wave flow. J. Nonlinear Sci. 8, 401–456.CrossRefGoogle Scholar
Milne-Thompson, M. 1968 Theoretical Hydrodynamics. Dover.Google Scholar
O'Meara, M. M. & Mueller, T. J. 1987 Laminar separation bubble characteristics on an airfoil at low Reynolds numbers. AIAA J. 25, 1033–1041.CrossRefGoogle Scholar
Peng, J. & Dabiri, J. O. 2007 A potential-flow, deformable-body model for fluid-structure interactions with compact vorticity: application to animal swimming measurements. Exps. Fluids DOI: 10.1007/S00348-007-0315-1Google Scholar
Rom-Kedar, V., Leonard, A., Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–394.Google Scholar
Rom-Kedar, V., Wiggins, S. 1990 Transport in two-dimensional maps. Arch. Rat. Mech. Anal. 109, 239–298.CrossRefGoogle Scholar
Salman, H., Hesthaven, J. S., Warburton, T., Haller, G. 2007 Predicting transport by Lagrangian coherent structures with a high-order method. Theor. Comput. Fluid Dyn. 21, 39–58.Google Scholar
Shadden, S. C., Dabiri, J. O., Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.CrossRefGoogle Scholar
Shadden, S. C., Lekien, F., Marsden, J. E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212, 271–304.Google Scholar
Shariff, K., Leonard, A. & Ferziger, J. H. 1989 Dynamics of a class of vortex rings. NASA Tech. Mem. 102257.Google Scholar
Shariff, K., Leonard, A. & Ferziger, J. H. 2006 Dynamical systems analysis of fluid transport in time-periodic vortex ring flows. Phys. Fluids 18, 047104.CrossRefGoogle Scholar
Shariff, K., Pulliam, T. H. & Ottino, J. M. 1991 A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder. Lectuces in Applied Mathematics, vol. 28 (ed. Allgower, E. L., Georg, K. & Miranda, R.). pp. 613–646. Springer.Google Scholar
Sturtevant, B. 1981 Dynamics of turbulent vortex rings. AFOSR-TR-81-0400, available from Defense Technical Information Service, Govt. Accession. No. AD-A098111, Fiche N81-24027.Google Scholar
Taira, K. & Colonius, T. 2007 The immersed boundary method: a projection approach. J. Comput. Phys., submitted.CrossRefGoogle Scholar
Voth, G. A., Haller, G., Gollub, J. P. 2002 Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 88, 254501.Google Scholar
Wiggins, S. 2005 The dynamical systems approach to Langrangian transport in oceanic flows. Annu. Rev. Fluid Mech. 37, 295–328.CrossRefGoogle Scholar
Yamada, H. & Matsui, T. 1978 Preliminary study of mutual slip-through of a pair of vortices. Phys. Fluids 21 292–294.CrossRefGoogle Scholar