A numerical simulation of unsteady flow in a two-dimensional collapsible channel

Journal of Fluid Mechanics

Volumn 314, Issue , 1996, Pages 191-225

  Luo, X Y ^a   Pedley, T J ^a,b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHANNEL FLOW; COMPUTER SIMULATION; INTEGRATION; MEMBRANES; NUMERICAL METHODS; OSCILLATIONS; PIPE FLOW; REYNOLDS NUMBER; TENSILE PROPERTIES; VORTEX FLOW;

FLOW SEPARATION; RECIRCULATING EDDIES; SPINE METHOD; VORTICITY WAVES;

UNSTEADY FLOW;

CHANNELS; COLLAPSIBLE; SIMULATION-NUMERICAL; UNSTEADY FLOW;

EID: 0030149024     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096000286     Document Type: Article

References (49)

1. BERTRAM, C. D. 1982 Two modes of instability in a thick-walled collapsible tube conveying a flow. J. Biomech. 15, 223-224.
2. BERTRAM, C. D. 1986 Unstable equilibrium behaviour in collapsible tubes. J. Biomech. 19, 61-69.
3. BERTRAM, C. D. & PEDLEY, T. J. 1982 A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15, 39-50.
4. BERTRAM, C. D. & PEDLEY, T. J. 1983 Steady and unsteady separation in an approximately two-dimensional indented channel. J. Fluid Mech. 130, 315-345.
5. BERTRAM, C. D., RAYMOND, C. J. & PEDLEY, T. J. 1990 Mapping of instabilities for flow through collapsed tubes of different length. J. Fluids Struct. 4, 125-154.
6. BERTRAM, C. D., RAYMOND, C. J. & PEDLEY, T. J. 1991 Application of nonlinear dynamics concepts to the analysis of self-excited oscillations of a collapsible tube conveying a fluid. J. Fluids Struct. 5, 391-426.
7. BONIS, M. & RIBREAU, C. 1978 Etude de quelques propriétés de l'écoulement dans une conduite collabable. La Houille Blanche 3/4, 165-173.
8. BORGAS, M. S. 1986 Waves, singularities and non-uniqueness in channel and pipe flows. PhD thesis, Cambridge University.
9. BROWER, R. W. & SCHOLTEN, C. 1975 Experimental evidence on the mechanism for the instability of flow in collapsible vessels. Med. Biol. Engng 13, 839-845.
10. CANCELLI, C. & PEDLEY, T. J. 1985 A separated-flow model for collapsible-tube oscillations. J. Fluid Mech. 157, 375-404.
11. 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, 199-232.
12. CARPENTER, P. W. & MORRIS, P. J. 1990 The effect of anisotropic wall compliance on boundary-layer stability and transition. J. Fluid Mech. 218, 171-223.
13. DAVIES, C. 1995 Evolution of Tollmien-Schlichting waves over a compliant panel. PhD thesis, University of Warwick.
14. DAVIES, C. & CARPENTER, P. W. 1995 Numerical simulation of the evolution of Tollmien-Schlichting waves over finite compliant panels. J. Fluid Mech. (submitted).
15. DAVIES, C. & CARPENTER, P. W. 1996 Instabilities in a panel channel flow between compliant walls. to be submitted.
16. EHRENSTEIN, U. & KOCH, W. 1989 Three-dimensional wavelike equilibrium states in plane Poiseuille flow. J. Fluid Mech. 228, 111-148.
17. ENGELMAN, M. S., SANI, R. L. & GRESHO, P. M. 1982 The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow. Intl J. Numer. Meth. Fluids 2, 225-238.
18. GRESHO, P. M., LEE, R. L. & SANI, R. L. 1979 On the time-dependent solutions of the Navier-Stokes equations in two and three dimensions. In Recent Advances in Numerical Methods in Fluids (ed. C. Taylor & K. Morgan), pp. 27-79.
19. GROTBERG, J. B. & REISS, E. L. 1984 Subsonic flapping flutter. J. Sound Vib. 92, 349-361.
20. GROTBERG, J. B. & SHEE, T. R. 1985 Compressible-flow channel flutter. J. Fluid Mech. 159, 175-193.
21. HOOD, P 1976 Frontal solution program for unsymmetric matrices. Intl J. Numer. Meth. Engng 10, 379-399.
22. IRONS, B. M. 1970 A frontal solution program for finite element analysis. Intl J. Numer. Meth. Engng 2, 5-32.
23. JENSEN, O. E. 1990 Instabilities of flow in a collapsed tube. J. Fluid Mech. 220, 623-659.
24. JENSEN, O. E. 1992 Chaotic oscillations in a simple collapsible tube model. J. Biomech. Engng 114, 55-59.
25. KATZ, A. I., CHEN, Y. & MORENO, A. H. 1969 Flow through a collapsible tube. Biophys. J. 9, 1261-1279.
26. KHESHGI, H. S. & SCRIVEN, L. E. 1984 Penalty finite element analysis of unsteady free surface flows. Finite Elements in Fluids 5 393-434.
27. KRAMER, M. O. 1962 Boundary layer stabilization by distributed damping. J. Am. Soc. Naval Engrs 74, 341-385.
28. LOWE, T. W., Luo, X. Y. & RAST, M. P. 1995 A comparison of three solution methods for flow in a collapsible channel. J. Fluids Struct, (submitted).
29. LOWE, T. W. & PEDLEY, T. J. 1995 Computation of Stokes flow in a channel with a collapsible segment. J. Fluids Struct. 9, 885-905.
30. LUCEY, A. D. & CARPENTER, P. W. 1992 A numerical simulation of the interaction of a compliant wall and inviscid flow. J. Fluid Mech. 234, 147-170.
31. LUO, X. Y. & PEDLEY, T. J. 1995 A numerical simulation of steady flow in a 2-D collapsible channel. J. Fluids Struct. 9, 149-174.
32. MATSUZAKI, Y. & FUNG, Y. C. 1979 Nonlinear stability analysis of a two-dimensional model of an elastic tube conveying a compressible flow. J. Appl. Mech. 46, 31-36.
33. MATSUZAKI, Y. & MATSUMOTO, T. 1989 Flow in a two-dimensional collapsible channel with rigid inlet and outlet. J. Biomech. Engng 111, 180-184.
34. OHBA, K., YONEYAMA, N., SHIMANAKA Y. & MAEDA, H. 1984 Self-excited oscillation of flow in collapsible tube. Tech. Rep. Kansai Univ. 25, 1-13.
35. ORSZAG, S. A. & PATERA, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347-385.
36. PEDLEY, T. J. 1992 Longitudinal tension variation in collapsible channels: a new mechanism for the breakdown of steady flow. J. Biomech. Engng 114, 60-67.
37. 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.
38. RALPH, M. E. & PEDLEY, T. J. 1988 Flow in a channel with a moving indentation. J. Fluid Mech. 190, 87-112.
39. RALPH, M. E. & PEDLEY, T. J. 1989 Viscous and inviscid flows in a channel with a moving indentation. J. Fluid Mech. 109, 543-566.
40. RALPH, M. E. & PEDLEY, T. J. 1990 Flow in a channel with a time-dependent indentation in one wall. J. Fluids Engng 112, 468-475.
41. RAST, M. P. 1994 Simultaneous solution of the Navier-Stokes and elastic membrane equations by a finite-element method. Intl J. Numer. Meth. Fluids 19, 1115-1135.
42. REYN, J. W. 1974 On the mechanism of self-excited oscillations in the flow through collapsible tubes. Delft Prog. Rep. 1, 51-67.
43. RILEY, J. J., GAD-EL-HAK, M. & METCALFE, R. W. 1988 Compliant coatings. Ann. Rev. Fluid Mech. 20, 393-420.
44. RUSCHAK, K. J. 1980 A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. Intl J. Numer. Meth. Engng 15, 639-648.
45. SAITO, H. & SCRIVEN, L. E. 1981 Studying of coating flow by the finite element method. J. Comput. Phys. 42, 53-76.
46. SCHOENDORFER, D. W. & SHAPIRO, A. H. 1977 The collapsible tube as a prosthetic vocal source. Proc. San Diego Biomed. Symp. 16, 349-356.
47. SHAPIRO, A. H. 1977 Steady flow in collapsible tubes. J. Biomech. Engng 99, 126-147.
48. SILLIMAN, W. J. 1979 Viscous film flows with contact lines. PhD thesis, University of Minnesota.
49. WEAVER, D. S. & PAIDOUSSIS, M. P 1977 On collapse and flutter phenomena in thin tubes conveying fluid. J. Sound Vib. 50, 117-132.