Fluid flow through a helical pipe

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 58, Issue 1, 2007, Pages 81-99

  Marušić Paloka, Eduard ^a   Pažanin, Igor ^a  

^a UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Asymptotic analysis; Curvilinear coordinates; Helical pipe; Navier Stokes equations

Indexed keywords

EID: 33845796676     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-006-0073-6     Document Type: Article

References (36)

1. Aganović, I., An introduction to boundary valus problems of continuum mechanics, Element, Zagreb, 2003 (in Croatian).
2. Back L. H., Banerjee R. K., Estimated flow resistance in a spiral coronary artery segment, J. Biol. Eng. 122 (2000), 675-677.
3. Bensoussan A., Lions J. L., Papanicolaou G. C., Asymptotic Analysis for Periodic Structures, North Holland, 1978.
4. Bogovski M. E., Solution of the first boundary problem for the equation of continuity of an incompressible medium, Soviet. Math. Dokl. 20 (1979), 1094-1098.
5. Bourgeat A., Marušić-Paloka E., Loi d'écoulement non linéaire entre deux plaques ondulées, C. R. Acad. Sci.Paris, Série I, t.321 (1995), 1115-1120.
6. 3 AS), 9(8)(1998), 1-25.
7. Dean W. R., Note on the motion of fluid in a curved pipe, Phil. Mag. 4 (7) (1927), 208-223.
8. Dean W. R., The stream-line motion of fluid in a curved pipe, Phil. Mag. 5 (7) (1928), 673-695.
9. Galdi G. P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol I, Springer-Verlag, Berlin 1994.
10. Germano M., On the effect of torsion on a helical pipe flow, J. Fluid Mech. 125 (1982), 1-8.
11. Germano M., The Dean equations extended to a helical pipe flow, J. Fluid Mech. 203 (1989), 289-305.
12. Gipouloux O., Marušić-Paloka E., Asymptotic behaviour of the incompressible Newtonian flow through thin constricted fracture, proceedings of the conference Multiscale problems in science and technology, Dubrovnik, 2000., Springer.
13. Heywood J.G., Rannacher R., Turek S., Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 22 (1996), 325-352.
14. Holland-Batt A.B., Spiral separation, theory and simulations, Trans. instn. Min. Metall 98 (1989), 46-60.
15. Hüttl T. J., Wagner C., Friedrich R., Navier-Stokes solutions of a laminar flows based on orthogonal helical co-ordinates, Int. J. Numer. Meth. Fluids 29 (1999), 749-763.
16. Hüttl T. J., Friedrich R., Influence of curvature and torsion on turbulent flow in helically coiled pipes, Engineering turbulence modelling and experiments 4, W. Rodi and D. Laurence eds., Elsevier Science, 1999, 247-256.
17. Jamal R., Sanchez-Palencia E., Théorie asymptotique des tiges courbes anisotropes, C. R. Acad. Sci. Paris, Série I, t.322 (1996), 1099-1106.
18. Jurak M., Tambaca J., Derivation and justification of a curved rod model, Math. Models Methods Appl.Sci. 9 (7) (1999), 991-1014.
19. Landau L., Lifchitz E., Physique théorique: Mécanique des Fluides, Séme édition, Ellipses, 1994.
20. Larrain J., Bonilla C. F., Theoretical analysis of pressure drop in the laminar flow of fluid in a coiled pipe. Trans. Soc. Rheol. 14 (1970), 135-147.
21. Marušić S., The asymptotic behaviour of quasi-Newtonian flow through a very thin or a very long curved pipe, Asymptotic Analysis 26 (1) (2001), 73-89.
22. Marušić S., Marušić-Paloka E., Two-scale convergence for thin domains and its applications to some lower-dimensional models in fluid mechanics, Asymptotic Analysis 23 (1)(2000), 23-58.
23. Marušić-Paloka E., The effects of flexion and torsion for a fluid flow through a curved pipe, Appl. Math. Opt. 44 (2001), 245-272.
24. Marušić-Paloka E., Fluid flow through a network of thin pipes, C. R. Acad. Sci. Paris, Série II b, t. 329 (2001), 1-6.
25. Marušić-Paloka E., Rigorous justification of the Kirchhoff law for junction of thin pipes filled with viscous fluid, Asymptotic Analysis 33 (1) (2003), 51-66.
26. Marušić-Paloka E., Incompressible Newtonian flow through thin pipes, proceedings of the conference Applied Mathematics and Scientific Computing, Dubrovnik 2001., Kluwer, 2003, 123-142.
27. Marušić-Paloka E., Marušić S., Computation of the permeability tensor for a fluid flow through a periodic net of thin channels, Appl. Anal. 64 (1997), 27-37.
28. Marušić-Paloka E., Pažanin I., Effective flow of a viscous liquid through a helical pipe, C. R. Mécanique, 332 (2004), 973-978.
29. Nazarov S. A., Piletskas K. I., The Reynolds flow in a thin three-dimensional channel, Lithuanian Math. J. 30 (1991), 366-375.
30. Trivedi R. N., Vasudeva K., Axial dispersion in laminar flow in helical coils. Chem Engrg. Sci. 30 (1975), 317-325.
31. Truesdell L. C., Adler R. J., Numerical treatment of fully developed laminar flow in helically coiled tubes, A. I. Ch. E. J. 16 (1970), 1010-1015.
32. Wang J-W., Andrews J. R. G., Numerical simulation of flow in helical ducts, A. I. Ch. E. J. 41 (5) (2004), 1071-1080.
33. Wang C. Y., On the low-Reynolds-number flow in a helical pipe, J. Fluid Mech. 108 (1981), 185-194.
34. K. Yamamoto K., S. Yanase S., and T. Yoshida T., Torsion effect on the flow in a helical pipe, Fluid Dyn. Res. 14 (1994), 259-273.
35. Zabielski L., Mestel A.J., Steady flow in a helically symmetric pipe, J. Fluid Mech. 370 (1998), 297-320.
36. Zhang J., Zhang B., Dean equations extended to a rotating helical pipe flow, J. Engrg. Mech. 129 (7) (2003), 823-829.