A Bifurcation Study of Laminar Flow in A Curved Tube of Rectangular Cross-Section

Journal of Fluid Mechanics

Volumn 180, Issue , 1987, Pages 343-369

  Winters, Keith H ^a  

^a Harwell Lab   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; MATHEMATICAL TECHNIQUES - NUMERICAL METHODS; TUBES;

BIFURCATION STUDY;

FLOW OF FLUIDS;

EID: 0023091554     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112087001848     Document Type: Article

References (31)

1. Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous fluid. Proc. R. Soc. Lond. A 59, 1–26.
2. Cheng, K. C., Lin, R. -C. & Ou, J. -W. 1976 Fully-developed laminar flow in curved rectangular channels. Trans. ASME I: J. Fluids Engng 98, 41–48.
3. Cliffe, K. A. 1983 Numerical calculations of two-cell and single-cell Taylor flows. J. Fluid Mech. 135, 219–233.
4. Cliffe, K. A. 1984 Numerical calculations of the primary flow exchange process in the Taylor Problem. Harwell Rep. AERE TP. 1060.
5. Cliffe, K. A. & Mullin, T. 1985 A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243–258.
6. Cliffe, K. A. & Spence, A. 1984 The calculation of high order singularities in the finite Taylor problem. In Numerical Methods for Bifurcation Problems (ed. T. Kupper, H. D. Mittleman & H. Weber). Birkhauser: ISNM.
7. Cliffe, K. A. & Winters, K. H. 1983 The Moore algorithm for bifurcation point location: its application to natural convection using the finite element code TGSL. Harwell Rep. AERE M. 3352.
8. Cliffe, K. A. & Winters, K. H. 1984 A numerical study of the cusp catastrophe for Benard convection in tilted cavities. J. Comp. Phys. 54, 531–534.
9. Cliffe, K. A. & Winters, K. H. 1986 The use of symmetry in bifurcation calculations and its application to the Benard problem. J. Comp. Phys. 67, 310–326.
10. Dean, W. R. 1928 The stream line motion of fluid in a curved pipe. Phil. Mag. 5, 673–695.
11. Dennis, S. C. R. & Ng, M. 1982 Dual solutions for steady laminar flow through a curved tube. Q. J. Mech. Appl. Math. 35, 305–324.
12. De Vriend, H. J. 1981 Velocity redistribution in curved rectangular channels. J. Fluid Mech. 107, 423–439.
13. Ghia, K. N. & Sokhey, J. S. 1977 Laminar incompressible viscous flow in curved ducts of regular cross-section. Trans. ASME I: J. Fluids Engng 99, 640–648.
14. Hille, P., Vehrenkamp, R. & Schulz-Dubois, E. O. 1985 The development and structure of primary and secondary flow in a curved square duct. J. Fluid Mech. 151, 219–241.
15. Keller, H. B. 1977 Numerical solutions of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359–384. Academic.
16. Jackson, C. P. & Winters, K. H. 1984 A finite-element study of the Benard problem using parameter-stepping and bifurcation search. Intl J. Num. Meth. Fluids 4, 127–145.
17. Jepson, A. & Spence, A. 1984 Singular points and their computation. In Numerical Methods for Bifurcation Problems (ed. T. Kiipper, H. D. Mittleman & H. Weber). Birkhauser: ISNM.
18. Jepson, A. & Spence, A. 1985 Folds in solutions of two parameter systems and their calculation. Part I. SIAM J. Numer. Anal. 22, 736–759.
19. Joseph, B., Smith, E. P. & Adler, R. J. 1975 Numerical treatment of laminar flow in helically coiled tubes of square cross-section. AIChE J. 21, 965–974.
20. Manlapaz, R. L. & Churchill, S. W. 1980 Fully developed laminar flow in a helically coiled tube of finite pitch. Chem. Engng Commun. 7, 57–78.
21. Masliyah, J. H. 1980 On laminar flow in curved semicircular ducts. J. Fluid Mech. 99, 469–479.
22. Moore, G. & Spence, A. 1980 The calculation of turning points of non-linear equations. SIAM J. Numer. Anal. 17, 567–576.
23. Nandakumar, K. & Masliyah, J. H. 1982 Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 119, 475–490.
24. Roose, D. & Caluwaerts, R. 1984 Direct methods for the computation of a nonsimple turning point corresponding to a cusp. In Numerical Methods for Bifurcation Problems (ed. T. Kiipper, H. D. Mittleman & H. Weber). Birkhauser: ISNM.
25. Spence, A. & Jepson, A. 1984 The numerical calculation of cusps, bifurcation points and isola formation points in two parameter problems. In Numerical Methods for Bifurcation Problems (ed. T. Kiipper, H. D. Mittleman & H. Weber). Birkhauser: ISNM.
26. Thomson, J. 1876 On the origin of windings of rivers in alluvial plains, with remarks on the flow of water round bends in pipes. Proc. R. Soc. Lond. A 25, 5–8.
27. Werner, B. 1984 Regular systems for bifurcation points with underlying symmetries. In Numerical Methods for Bifurcation Problems (ed. T. Kiipper, H. D. Mittleman & H. Weber). Birkhauser: ISNM.
28. Werner, B. & Spence, A. 1984 The computation of symmetry-breaking bifurcation points. SIAM J. Numer. Anal. 21, 388–399.
29. Winters, K. H. & Brindley, R. C. G. 1984 Multiple solutions for laminar flow in helically-coiled tubes. Harwell Rep. AERE R. 11373.
30. Winters, K. H. & Cliffe, K. A. 1985 Convergence properties of the finite-element method for Benard convection in an infinite layer. J. Comp. Phys. 60, 346–351.
31. Winters, K. H., Cliffe, K. A. & Jackson, C. P. 1984 A review of extended systems for finding critical points in coupled problems. In Numerical Methods for Transient and Coupled Problems (ed. R. W. Lewis, E. Hinton, P. Bettess and B. A. Schrefler). Swansea: Pineridge.