Computational flow in a collapsed tube with wall contact

Mecanique et Industries

Volumn 1, Issue 4, 2000, Pages 349-364

  Thiriet, Marc ^a   Ribreau, Christian ^b  

^a INRIA   (France)

^b LGMPB   (France)

Author keywords

Collapsed tube flow; Contact; Finite element method; Jet; Model; One dimensional theory; Three dimensional flow; Tube

Indexed keywords

EID: 0034215692     PISSN: 12962139     EISSN: None     Source Type: Journal    
DOI: 10.1016/s1296-2139(00)01043-5     Document Type: Article

References (56)

1. Bonis M., Ribreau C., Verchery G., Étude théorique et expérimentale de l'aplatissement d'un tube élastique en dépression, J. Mec. Appl. 5 (1981) 123-144.
2. Dion B., Naili S., Renaudeaux J.P., Ribreau C., Buckling of elastic tubes: Study of highly compliant device, Med. Biol. Eng. Comput. 33 (1995) 196-201.
3. Begis D., Delpuech C., Le Tallec P., Loth L., Thiriet M., Vidrascu M., A finite element model of tracheal collapse, J. Appl. Physiol. 64 (1988) 1359-1368.
4. Thiriet M., Maarek J.M., Chartrand D.A., Delpuech C., Davis L., Hatzfeld C., Chang H.K., Transverse images of the human thoracic trachea during forced expiration, J. Appl. Physiol. 67 (1989) 1032-1040.
5. Flaherty J.E., Keller J.B., Rubinow S.I., Post buckling behavior of elastic tubes and rings with opposite sides in contact, SIAM J. Appl. Math. 23 (1972) 446-455.
6. Kresch E., Compliance of flexible tubes, J. Biomech. 12 (1979) 825-839.
7. Ribreau C., Naili S., Bonis M., Langlet A., Collapse of thin-walled elliptical tubes for high values of major-to-minor axis ratio, ASME J. Biomech. Eng. 115 (1993) 432-440.
8. Nahmias J., Pertes de Charge dans les Tuyaux Collabables, Thèse, Université Paris VI, 1980.
9. Kresch E., Noordegraaf A., Cross-sectional shape of collapsible tubes, Biophys. J. 12 (1972) 274-294.
10. Bonis M., Ribreau C., Wave speed in noncircular collapsible ducts, ASME J. Biomech. Eng. 103 (1981) 27-31.
11. Thiriet M., Delpuech C., Piroird J.M., Magnin I., Banc de mesure optique de la déformation de conduites souples, Innov. Technol. Biol. Med. 8 (1987) 99-107.
12. Elad D., Sahar M., Avidor J., Einav S., Steady flow through collapsible tubes: Measurements of flow and geometry, ASME J. Biomech. Eng. 114 (1992) 84-91.
13. Kececioglu I., MacClurken M.E., Kamm R.D., Shapiro A.H., Steady supercritical flow in collapsible tube: 1. Experimental observations, J. Fluid Mech. 109 (1981) 367-389.
14. Bertram C.D., Ribreau C., Cross-sectional area measurements in collapsed tubes using the transformer principle, Med. Biol. Eng. Comput. (1989) 357-364.
15. Ribreau C., Merle D., Bonis M., Détermination expérimentale du module d'Young transversal d'une conduite élastique en dépression lors de son aplatissement. Conditions d'application aux veines, J. Biophysique Biomécanique 10 (1986) 57-62.
16. Shapiro A.H., Steady flow in collapsible tubes, ASME J. Biomech. Eng. 99 (1977) 126-147.
17. Ribreau C., Sur la Loi D'état, la Loi de Perte de Charge, et la Nature de L'écoulement Permanent en Conduite Collabable Inclinée, Thèse, Université Paris XII, 1991.
18. Knowlton F.P., Starling E.H., The influence of variation in temperature and blood pressure on the performance of the isolated mammalian heart, J. Physiol. 44 (1912) 206-219.
19. Rodbard S., Saiki H., Flow through collapsible tubes, American Heart J. 46 (1953) 715-725.
20. Holt J.P., Flow of liquids through collapsible tubes, Circ. Res. 7 (1959) 342-353.
21. Bonis M., Ribreau C., Étude de quelques propriétés de l'écoulement dans une conduite collabable, La Houille Blanche 3/4 (1978) 165-173.
22. Lyon C.K., Scott J.B., Wang C.Y., Flow through collapsible tubes at low Reynolds numbers. Applicability of the waterfall model, Circ. Res. 47 (1980) 68-73.
23. Bertram C.D., Unstable equilibrium in collapsible tubes, J. Biomech. 19 (1986) 61-69.
24. Bertram C.D., Raymond C.J., Pedley T.J., Mapping of instabilities for flow through collapsed tubes of differing length, J. Fluids Struct. 4 (1990) 125-153.
25. Fry D.L., Theoretical considerations of the bronchial pressure flow-volume relationships with particular reference to the maximum expiratory flow-volume curve, Phys. Med. Biol. 3 (1958) 174-194.
26. Conrad W.A., Pressure-flow relationships in collapsible tubes, IEEE Trans. Biomed. Eng. 16 (1969) 284-295.
27. Kamm R.D., Shapiro A.S., Unsteady flow in a collapsible tube subjected to external pressure, J. Fluid Mech. 95 (1979) 1-78.
28. Thiriet M., Bonis M., Experiments on flow limitation during forced expiration in a monoalveolar lung model, Med. Biol. Eng. Comput. 21 (1983) 681-687.
29. Thiriet M., Bonis M., Adedjouma A.S., Hatzfeld C., Yvon J.P., Experimental and theoretical models of flow during forced expiration: Pressure and pressure history dependence of flow rate, Med. Biol. Eng. Comput. 25 (1987) 551-559.
30. Pedley T.J., Stephanoff K.D., Flow along a channel with a time-dependent indentation in one wall: The generation of vorticity waves, J. Fluid Mech. 160 (1985) 337-367.
31. Rubinow S.I., Keller J.B., Flow of a viscous fluid through an elastic tube with application to blood flow, J. Theor. Biol. 35 (1972) 299-313.
32. Wild R., Pedley T.J., Ridley D.S., Viscous flow in collapsible tubes of slowly varying cross-section, J. Fluid Mech. 81 (1977) 273-294.
33. Pedley T.J., The Fluid Mechanics of Large Blood Vessels, Cambridge University Press, Cambridge, UK, 1980.
34. Bertram C.D., Pedley T.J., A mathematical model of unsteady collapsible tube behaviour, J. Biomech. 15 (1982) 39-50.
35. Cancelli C., Pedley T.J., A separated flow model for collapsible tube oscillations, J. Fluid Mech. 157 (1985) 375-404.
36. Jensen O.E., Instabilities of flow in a collapsed tube, J. Fluid Mech. 220 (1990) 623-659.
37. Ribreau C., Naili S., Langlet A., Head losses in smooth pipes obtained from collapsed tubes, J. Fluids Struct. 8 (1994) 183-200.
38. Bonis M., Adedjouma A.S., personal communication.
39. Thiriet M., Bonis M., Adedjouma A.S., Yvon J.P., A numerical model of expired flow in a monoalveolar lung model subjected to pressure ramps, ASME J. Biomech. Eng. 111 (1989) 9-16.
40. Weaver D.S., Paidoussis M.P., On collapse and flutter phenomena in thin tubes conveying fluid, J. Sound Vibration 50 (1977) 117-132.
41. Matsuzaki Y., Fung Y.C., Stability analysis of straight and buckled two-dimensional channels conveying an incompressible flow, ASME J. Appl. Mech. 99 (1977) 548-552.
42. Grotberg J.B., Graviely N., Flutter in collapsible tubes: A theoretical model of wheezes, J. Appl. Physiol. 66 (1989) 2262-2273.
43. Matsuzaki Y., Ikeda T., Kitegawa T., Sakada S., Analysis of flow in a two-dimensional collapsible channel using universal tube law, ASME J. Biomech. Eng. 116 (1994) 469-476.
44. Ohba K., Sakurai A., Oka J., Self-excited Oscillations in Collapsible Tube. IV (Laser Doppler Measurement of Local Flow Field), Technol. Report, Kansai University, 1989.
45. Heil M., Pedley T.J., Large post-buckling deformations of cylindrical shells conveying viscous flow, J. Fluids Struct. 10 (1996) 565-599.
46. Benmbarek M., Écoulement Laminaire Permanent dans un Modèle de Veine, Thèse, Université Paris XII, 1997.
47. George P.L., Borouchaki H., Triangulation de Delaunay et maillage, Applications Aux Éléments Finis, Hermès, Paris, 1997.
48. Conca C., Pares C., Pironneau O., Thiriet M., A computational model of Navier-Stokes equations with imposed pressure and velocity fluxes, Internat. J. Numer. Methods Fluids 20 (1995) 267-287.
49. Arnold D.N., Brezzi F., Fortin M., A stable finite element for the Stokes equation, Calcolo 21 (1984) 337-344.
50. Pironneau O., On the transport-diffusion algorithm and its application to the Navier-Stokes equations, Numerische Mathematik 38 (1982) 309-332.
51. Glowinski R., Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New York, 1984.
52. Bertram C.D., Godbole S.A., LDA measurements of velocities in a simulated collapsed tube, ASME J. Biomech. Eng. 119 (1997) 357-363.
53. Luo X.Y., Pedley T.J., A numerical simulation of unsteady flow in a two-dimensional collapsible channel, J. Fluid Mech. 314 (1996) 191-225.
54. Heil M., Stokes flow in collapsible tubes: Computation and experiment, J. Fluid Mech. 353 (1997) 285-312.
55. Ribreau C., Bonis M., Propagations et écoulements dans les tubes collabables. Contributions à l'étude des vaisseaux sanguins, J. Fr. Biophysique Médecine Nucléaire 3 (1978) 153-158.
56. Taylor L.A., Gerrard J.H., Pressure radius relationships for elastic tubes and their application to arteries, Med. Biol. Eng. Comput. 15 (1977) 11-21.