The energetics of flow through a rapidly oscillating tube. Part 1. General theory

Journal of Fluid Mechanics

Volumn 648, Issue , 2010, Pages 83-121

  Whittaker, Robert J ^a   Waters, Sarah L ^a   Jensen, Oliver E ^b   Boyle, Jonathan ^c   Heil, Matthias ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; BUDGET CONTROL; ENERGY TRANSFER; FLOW RATE; STROUHAL NUMBER; SYSTEM STABILITY;

ARBITRARY CROSS SECTION; ASYMPTOTIC EXPRESSIONS; BACKGROUND FLOW; FUNDAMENTAL MECHANISMS; SELF EXCITED OSCILLATION; THIN BOUNDARY LAYERS; WALL OSCILLATIONS; WOMERSLEY NUMBERS;

OSCILLATING FLOW;

ENERGY FLUX; FLOW STABILITY; FLUID MECHANICS; OSCILLATING FLOW; PIPE FLOW; VISCOSITY;

EID: 77952414032     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009992904     Document Type: Article

References (27)

1. Aris, R. 1962 Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Prentice-Hall.
2. Avrahami, I. D. I. T. & Gharib, M. 2008 Computational studies of resonance wave pumping in compliant tubes. J. Fluid Mech. 608, 139-160.
3. Bertram, C. D. 2003 Experimental studies of collapsible tubes. In Flow Past Highly Compliant Boundaries and in Collapsible Tubes (ed. P. W. Carpenter & T. J. Pedley), chap. 3, pp. 51-65. Kluwer Academic.
4. Bringley, T. T., Childress, S., Vandenberghe, N. & Zhang, J. 2008 An experimental investigation and a simple model of a valveless pump. Phys. Fluids 20, 033602.
5. Floryan, J. F. 2003 Vortex instability in a diverging-converging channel. J. Fluid Mech. 482, 17-50.
6. Floryan, J. F., Szumbarski, J. & Wu, X. 2002 Stability of flow in a channel with vibrating walls. Phys. Fluids 14, 3927-3936.
7. Gao, P. & Lu, X.-Y. 2006 Instability of channel flow with oscillatory wall suction/blowing. Phys. Fluids 18, 034102.
8. Grotberg, J. B. & Jensen, O. E. 2004 Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech. 36, 121-147.
9. Heil, M. & Jensen, O. E. 2003 Flows in deformable tubes and channels: theoretical models and biological applications. In Flow Past Highly Compliant Boundaries and in Collapsible Tubes (ed. P. W. Carpenter & T. J. Pedley), chap 2, pp. 15-49. Kluwer Academic.
10. Heil, M. & Waters, S. L. 2006 Transverse flows in rapidly oscillating elastic cylindrical shells. J. Fluid Mech. 547, 185-214.
11. Heil, M. & Waters, S. L. 2008 How rapidly oscillating collapsible tubes extract energy from a viscous mean flow. J. Fluid Mech. 601, 199-227.
12. Hickerson, A., Rinderknecht, D. & Gharib, M. 2005 Experimental study of the behaviour of a valveless impedance pump. Exper. Fluids 39 (4), 787.
13. Hickerson, A. I. & Gharib, M. 2006 On the resonance of a pliant tube as a mechanism for valveless pumping. J. Fluid Mech. 555, 141-148.
14. Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.
15. Jensen, O. E. & Heil, M. 2003 High-frequency self-excited oscillations on a collapsible-channel flow. J. Fluid Mech. 481, 235-268.
16. Jovanovic, M. R. 2008 Turbulence suppression in channel flows by small amplitude transverse wall oscillations. Phys. Fluids 20, 014101.
17. Jovanovic, M. R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145-183.
18. Liebau, G. 1954 Uber ein ventilloses Pumpprinzip. Naturwissenschaften 41, 327.
19. Luo, X. Y., Cai, Z., Li, W. G. & Pedley, T. J. 2008 The cascade structure of linear instability in collapsible channel flows. J. Fluid Mech. 600, 45-76.
20. Luo, X. Y. & Pedley, T. J. 1996 A numerical simulation of unsteady flow in a two-dimensional collapsible channel. J. Fluid Mech. 314, 191-225.
21. Pedley, T. J. & Stephanoff, K. D. 1985 Flow along a channel with a time-dependent indentation: the generation of vorticity waves. J. Fluid Mech. 160, 337-367.
22. Ralph, M. E. & Pedley, T. J. 1988 Flow in a channel with a moving indentation. J. Fluid Mech. 190, 87-112.
23. Smith, F. T. 1976a Flow through constricted or dilated pipes and channels. Part 1. Q. J. Mech. Appl. Math. 29, 343-364.
24. Smith, F. T. 1976b Flow through constricted or dilated pipes and channels. Part 2. Q. J. Mech. Appl. Math. 29, 365-376.
25. Stewart, P. S., Waters, S. L. & Jensen, O. E. 2009 Local and global instabilities of flow in a flexible-walled channel. Eur. J. Mech. B. Fluids 28 (4), 541-557.
26. Szumbarski, J. & Floryan, J. M. 2006 Transient disturbance growth in a corrugated channel. J. Fluid Mech. 568, 243-272.
27. Whittaker, R. J., Heil, M., Boyle, J., Jensen, O. E. & Waters, S. L. 2010 The energetics of flow through a rapidly oscillating tube. Part 2. Application to an elliptical tube. J. Fluid Mech. 648, 123-153.