The cascade structure of linear instability in collapsible channel flows

Journal of Fluid Mechanics

Volumn 600, Issue , 2008, Pages 45-76

  Luo, X Y ^a   Cai, Z X ^b   Li, W G ^c   Pedley, T J ^d  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b TIANJIN UNIVERSITY   (China)

^c UNIVERSITY OF SHEFFIELD   (United Kingdom)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CASCADES (FLUID MECHANICS); CHANNEL FLOW; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FLOW STRUCTURE; REYNOLDS NUMBER; STIFFNESS; STRAIN; UNSTEADY FLOW;

ORR-SOMMERFELD EQUATIONS; SELF-EXCITED OSCILLATIONS; SOLID MECHANICS;

FLUID STRUCTURE INTERACTION;

CASCADES (FLUID MECHANICS); CHANNEL FLOW; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FLOW STRUCTURE; FLUID STRUCTURE INTERACTION; REYNOLDS NUMBER; STIFFNESS; STRAIN; UNSTEADY FLOW;

ANALYTICAL METHOD; CHANNEL FLOW; COMPUTER SIMULATION; FLOW MODELING; FLOW STABILITY; FLOW STRUCTURE; OSCILLATING FLOW; REYNOLDS NUMBER;

EID: 41549145795     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008000293     Document Type: Article

References (56)

1. BARRODALE, I. & WILSON, K. B. 1978 A Fortran program for solving a nonlinear equation by Muller's method. J. Comput. Appl. Maths 4 (2), 159-166.
2. BEARMAN, P. W. & HUARTE, F. H. 2006 The hydrodynamic forces acting on long flexible circular cylinder responding to VIV. Proc. 6th FSI, AE & FIV and N Symp. Vancouver.
3. BERTRAM, C. D. 1982 Two modes of instability in a thick-walled collapsible tube conveying a flow. J. Biomech. 15, 223-224.
4. BERTRAM, C. D. & ELLIOTT, N. S. J. 2001 Aqueous flow limitation in uniform collapsible tubes: Multiple flow-limited flow-rates at the same pressure drop and upstream transmural pressure. Proc. ASME Bioengng Conf. 27 June-1 July, Snowbird, vol. 50 (ed. R. D. Kamm, G. W. Schmid-Shonbein, G. A. Ateshian & M. S. Hefzy), pp. 383-384.
5. BERTRAM, C. D., RAYMOND, C. J. & PEDLEY, T. J. 1990 Mapping of instabilities for flow through collapsed tubes of differing length. J. Fluids Struct. 4, 125-153.
6. CAI, Z. X. & LOU, X. Y. 2003 A fluid-beam model for flow in a collapsible channel. J. Fluids Struct. 17, 125-146.
7. CANCELLI, C. & PEDLEY, T. J. 1985 A separated-flow model for collapsible-tube oscillations. J. Fluid Mech. 157, 375-404.
8. CARPENTER, P. W. & GARRAD, A. D. 1986 The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech. 170, 188-232.
9. DAVIES, C. & CARPENTER, P. W. 1997a Numerical simulation of the evolution of Tollmien-Schlichting waves over finite compliant panels. J. Fluid Mech. 335, 361-392.
10. DAVIES, C. & CARPENTER, P. W. 1997b Instabilities in a plane channel flow between compliant walls. J. Fluid Mech. 352, 205-243.
11. DAVIES, C., CARPENTER, P. W., ALI, R. & LOCKERBY, D. A. 2006 Disturbance development in boundary layers over compliant surfaces. Laminar-Turbulent Transition, IUTAM Symp. Bangalore, India (ed. R. Govindarajan). pp. 225-230. Springer.
12. EHRENSTEIN, U. & ROSSI, M. 1993 Nonlinear Tollmien-Schlichting waves for plane Poiseuille flow with compliant walls. Eur. J. Mech. B/Fluids 12, 789-810.
13. GARBOW, B. S. 1978 The QZ algorithm to solve the generalized eigenvalue problem for complex matrices. ACM Trans. Math. Software 4, 404-410.
14. GREEN, C. H. & ELLEN, C. H. 1972 The stability of plane Poiseuille flow between flexible walls. J. Fluid Mech. 51, 403-416.
15. GRIMSHAW, R. 1990 Nonlinear Ordinary Differential Equations. Blackwell Scientific/Wolfe.
16. GROTBERG, J. B. & GAVRIELY, N. 1989 Flutter in collapsible tubes: a theoretical model of wheezes. J. Appl. Physiol. 66, 2262-2273.
17. GUNERATNE, J. C. & PEDLEY T. J. 2006 High-Reynolds number steady flow in a collapsible channel. J. Fluid Mech. 569, 151-184.
18. HAUGHTON, D. 1980 Post-bifurcation of perfect and imperfect spherical elastic membranes. Intl J. Solid Struct. 16, 1123-1133.
19. HAYASHI, S., HAYASE, T. & KAWAMURA, H. 1998 Numerical analysis for stability and self-excited oscillation in collapsible tube flow. Trans. ASME K: J. Biomech. Engng 120, 468-475.
20. HAZEL, A. L. & HEIL, M. 2003 Steady finite-Reynolds-n umber flows in three-dimensional collapsible tubes. J. Fluid Mech. 486, 79-103.
21. HEIL, M. 1997 Stokes flow in collapsible tubes: Computation and experiment. J. Fluid Mech. 353, 285-312.
22. HEIL, M. & WATERS, S. L. 2006 Transverse flows in a rapidly oscillating, elastic cylindrical shell. J. Fluid Mech. 547, 185-214.
23. HEMON, P., DE LANGRE, E. & SCHMID, P. 2006 Experimental evidence of transient growth of energy before airfoil flutter. J. Fluids Struct. 22, 391-400.
24. JENSEN, O. E. 1990 Instabilities of flow in a collapsed tube. J. Fluid Mech. 220, 623-659.
25. JENSEN, O. E. 1992 Chaotic oscillations in a simple collapsible tube model. Trans. ASME K: J. Biomech. Engng 114, 55-59.
26. JENSEN, O. E. & HEIL, M. H. 2003 High-frequency self-excited oscillations in a collapsible-channel flow. J. Fluid Mech. 481 235-268.
27. JENSEN, O. E. & PEDLEY, T. J. 1989 The existence of steady flow in a collapsed tube. J. Fluid Mech. 206, 339-374.
28. KAMM, R. D. & PEDLEY, T. J. 1989 Flow in collapsible tubes: A brief review. Trans. ASME K: J. Biomech. Engng 111, 117-179.
29. DE LANGRE, E., PAIDOUSSIS, M. P., DOARE, O. & MODARESS-SADEGHI, Y. 2007 Flutter of long flexible cylinders in axial flow. J. Fluid Mech. 571, 371-389.
30. LIU, H. F., LUO, X. Y. & CAI, Z. X. 2007 Sensitivity of unsteady collapsible channel flows to modelling assumptions. Comput. Struct. (submitted).
31. LOPES, J. L., PAIDOUSSIS, M. P. & SEMLER, C. 2002 Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 2. The equations of motion. J. Fluids Struct. 16, 715-737.
32. LUCEY, A. D. & PITMAN, D. M. 2006 A new method for determining the eigenmodes of finite flow-structure systems. Proc. 6th FSI, AE & FIV and N Symp. Vancouver.
33. LOU, X. Y. & CAI, Z. X. 2004 Effects of wall stiffness on the linear stability of flow in an elastic channel. Proc. 8th Intl Conf. on Fluid Induced Vibrations, Paris, France (ed. E. de Langre & F. Axisa), vol. 2, pp. 167-170.
34. LOU, X. Y. & PEDLEY, T. J. 1995 A numerical simulation of steady flow in a two-dimensional collapsible channel. J. Fluids Struct. 9, 149-174.
35. LOU, X. Y. & PEDLEY, T. J. 1996 A numerical simulation of unsteady flow in a two-dimensional collapsible channel. J. Fluid Mech. 314, 191-225.
36. LOU, X. Y. & PEDLEY, T. J. 1998 The effects of wall inertia on flow in a two-dimensional collapsible channel. J. Fluid Mech. 363, 253-280.
37. LOU X. Y. & PEDLEY, T. J. 2000 Multiple solutions and flow limitation in two-dimensional collapsible channel flows. J. Fluid Mech. 420, 301-324.
38. LOU, X. Y., CALDERHEAD, B., LIU, H. F. & LI, W. G. 2007 On the initial configurations of collapsible channel flow. Comput. Struct. 85, 977-987.
39. MARZO, A. X. Y., LUO, X. Y. & BERTRAM, C. D. 2005 Three-dimensional flow through a thick walled collapsible tube. J. Fluids Struct. 20, 817-835.
40. MATSUZAKI, Y. & FUJIMURA, K. 1995 Reexamination of steady solutions of a collapsible channel conveying fluid, a technical brief. Trans. ASME K: J. Biomech. Engng 117, 492-494.
41. NAYFEH, A. H. 1973 Perturbation Methods. Wiley-Interscience.
42. PAIDOUSSIS, M. P. 1998 Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 1. Elsevier.
43. PAIDOUSSIS, M. P. 2004 Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 2. Elsevier.
44. PAIDOUSSIS, M. P., GRINEVICH, E., ADAMOVIC, D., & SEMLER, C. 2002 Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 1. Physical dynamics. J. Fluids Struct. 16, 691-713.
45. PEDLEY, T. J. 1980 The Fluid Mechanics of Large Blood Vessels Cambridge University Press.
46. PEDLEY, T. J. & LUO, X. Y. 1998 Modelling flow and oscillations in collapsible tubes. Theor. Comput. Fluid Dyn. 10, 277-294.
47. PEDLEY, T. J. & STEPHANOFF, K. D. 1985 Flow along a channel with a time-dependent indentation in one wall: The generation of vorticity waves. J. Fluid Mech. 160, 337-367.
48. PRESS, W. H., TEUKOLSKY S. A., VETTERLING, W. T. & FLANNERY, B. P. 2002 Numerical Recipes in Fortran, the Art of Scientific Computing 2nd edn. Cambridge University Press.
49. SEMLER, C., LOPES, J. L., AUGU, N. & PAIDOUSSIS, M. P. 2002 Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 3. Nonlinear dynamics. J. Fluids Struct. 16, 739-759.
50. SHAPIRO, A. H. 1977 Steady flow in collapsible tubes. Trans. ASME K: J. Biomech. Engng 99, 126-147.
51. TETLOW, A., LUCEY, A. D. & BALINT, T. S. 2006 Instability of a cantilevered flexible plate in viscous channel flow driven by constant pressure drop. Proc. 6th FSI, AE & FIV and N Symp. Vancouver.
52. TIMOSHENKO, A. P. & GERE, J. M. 1963 Theory of Elastic Stability, 2nd edn. McGraw-Hill.
53. WEBSTER, P. M., SAWATZKY, R. P., HOFFSTEIN, V., LEBLANG, R., HINCHEY, J. M. & SULLIVAN, P. A. 1985 Wall motion in expiratory flow limitation: Choke and flutter. J. Appl. Physiol. 59, 1304-1312.
54. WU, X. S. & LUO, J. S. 2006 Influence of small imperfections on the stability of plane Poiseuille flow and the limitation of Squire's theorem. Phys. Fluids 18, 044104.
55. YAMAKI, N. 1984 Elastic Stability of Circular Cylindrical Shells. North-Holland.
56. ZHU, Y. F., LUO, X. Y. & OGDEN, R. W. 2007 Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure. Intl J. Solids Struct. (accepted).