Skip to main content Accessibility help
×
×
Home

Aspect Ratio Effect on Laminar Flow Bifurcations in a Curved Rectangular Tube Driven by Pressure Gradients

  • K. T. Chen (a1), K. F. Yarn (a2), H. Y. Chen (a1), C. C. Tsai (a1), W. J. Luo (a3) and C. N. Chen (a4)...

Abstract

This study investigated the flow bifurcations of flows driven by a pressure gradient in a rectangular curved tube. When fluid flows within a curved tube, due to the centrifugal effect, secondary vortices can be induced in the cross section of the tube. The secondary flow states are dependent on the magnitude of the pressure gradient (q) and the aspect ratio (γ). In this study, the continuation method was applied to investigate the flow bifurcations in a curved tube with increasing pressure gradient (1 < q < 6000) and aspect ratio (0.9 < γ < 1.4).

The bifurcation diagrams are composed of solution branches, which are linked by limiting points or bifurcation points. The flow states in a solution branch belong to the same group. The ranges of the flow states and the relationship between the states can also be derived from the bifurcation diagrams. In this study, two types of bifurcation were found, one in the range of 0.9 < γ < 1.17, and another in the range of 1.18 < γ < 1.4. The ranges of stable flow solutions and the distributions of limit and bifurcation points in both pressure gradient and aspect ratio are derived in this study.

Copyright

Corresponding author

*Corresponding author (wjluo@ncut.edu.tw)

References

Hide All
1. Dean, W. R., “The Stream-Line Motion of Fluid in a Curved Pipe,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Series 7, 5, pp. 673695 (1928).
2. Joseph, B., Smith, E. P. and Adler, R. J., “Numerical Treatment of Laminar Flow in Helically Coiled Tubes of Square Cross-Section,” AIChE Journal, 21, pp. 965974 (1975).
3. Cheng, K. C., Lin, R. C. and Ou, J. W., “Fully-Developed Laminar Flow in Curved Rectangular Channels,” Journal of Fluids Engineering, 98, pp. 4148 (1976).
4. Hille, P., Vehrenkamp, R. and Schulz-Dubois, E. O., “The Development and Structure of Primary and Secondary Flow in a Curved Square Duct,” Journal of Fluid Mechanics, 151, pp. 219241 (1985).
5. Winters, K. H., “A Bifurcation Study of Laminar Flow in a Curved Tube of Rectangular Cross- Section,” Journal of Fluid Mechanics, 180, pp. 343369 (1987).
6. Gauthier, G., Gondret, P., Thomé, H. and Rabaud, M., “Centrifugal Instabilities in a Curved Rectangular Duct of Small Aspect ratio,” Physics of Fluids, 13, pp. 28312834 (2001).
7. Yanase, S., Kaga, Y. and Daikai, R., “Laminar Flow through a Curved Rectangular Duct over a Wide Range of the Aspect Ratio,” Fluid Dynamics Research, 31, pp. 151183 (2002).
8. Yamamoto, K., Wu, X., Hyakutake, T. and Yanase, S., “Taylor-Dean Flow through a Curved Duct of Square Cross Section,” Fluid Dynamics Research, 35, pp. 676–82 (2004).
9. Yamamoto, K., Wu, X., Nozaki, K. and Hayamizu, Y., “Visualization of Taylor-Dean Flow in a Curved Duct of Square Cross-Section,” Fluid Dynamics Research, 38, pp. 118 (2006).
10. Bhunla, A. and Chen, C. L., “Flow Characteristics in a Curved Rectangular Channel with Variable Cross-Sectional Area,” Journal of Fluid Engineering, 131, 091102 (2009).
11. Norouzi, M., Kayhani, M. H., Shu, C. and Nobari, M .R. H., “Flow of Second-Order Fluid in a Curved Duct with Square Cross-Section,” Journal of Non-Newtonian Fluid Mechanics, 165, pp. 323339 (2010).
12. Norouzi, M. and Biglari, N., “An Analytical Solution for Dean Flow in Curved Ducts with Rectangular Cross Section,” Physics of Fluids, 25, 053602 (2013).
13. Wang, L. and Yang, T., “Periodic Oscillation in Curved Duct Flows,” Physica D, 200, pp. 296302 (2005).
14. Mondal, R. N., Kaga, Y., Hyakutake, T. and Yanase, S., “Bifurcation Diagram for Two-Dimensional Steady Flow and Unsteady Solutions in a Curved Square Duct,” Fluid Dynamics Research, 39, pp. 413446 (2007).
15. Komai, Y. and Tanishita, K., “Fully Developed Intermittent Flow in a Curved Tube,” Journal of Fluid Mechanics, 347, pp. 263287 (1997).
16. Hüttl, T. J. and Friedrich, R., “Influence of Curvature and Torsion on Turbulent Flow in Helically Coiled Pipes,” International Journal of Heat and Fluid Flow, 21, pp. 345353 (2000).
17. Cioncolini, A. and Santini, L., “On the Laminar to Turbulent Flow Transition in Diabatic Helically Coiled Pipe Flow,” Experimental Thermal and Fluid Science, 30, pp. 653661 (2006).
18. Ko, T. H. and Ting, K., “Optimal Reynolds Number for the Fully Developed Laminar Forced Convection in a Helical Coiled Tube,” Energy, 31, pp. 21422152 (2006).
19. Liu, F. and Wang, L., “Analysis on Multiplicity and Stability of Convective Heat Transfer in Tightly Curved Rectangular Ducts,” International Journal of Heat and Mass Transfer, 52, pp. 58495866 (2009).
20. Mondal, R. N., Uddin, M. S. and Yanase, S., “Numerical Prediction of Non-Isothermal Flow through a Curved Square Duct,” International Journal of Fluid Mechanics Research, 37, pp. 8599 (2010).
21. Mondal, R. N., Islam, S., Uddin, K. and Hossain, A., “Effects of Aspect Ratio on Unsteady Solutions through Curved Duct Flow,” Applied Mathematics and Mechanics, 34, pp. 11071122 (2013).
22. Keller, H. B., Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems, In Applications of Bifurcation Theory, Rabinowitz, P. Ed., pp. 359384, Academic Press, New York (1977).
23. Yang, R.-J. and Luo, W.-J., “Flow Bifurcations in a Thin Gap between Two Rotating Spheres,” Theoretical and Computational Fluid Dynamics, 16, pp. 115131 (2002).
24. Luo, W.-J. and Yang, R.-J., “Multiple Fluid Flow and Heat Transfer Solutions in a Two-Sided Lid-Driven Cavity,” International Journal of Heat and Mass Transfer, 50, pp. 23942405 (2007).
25. Chen, K. T., Tsai, C. C., Luo, W. J. and Chen, C. N., “Multiplicity of Steady Solutions in a Two-Sided Lid-Driven Cavity with Different Aspect Ratios,” Theoretical and Computational Fluid Dynamics, 27, pp. 767776 (2013).
26. Chen, K. T., Tsai, C. C., Luo, W. J., Lu, C. W. and Chen, C. H., “Aspect Ratio Effect on Multiple Flow Solutions in a Two-Sided Parallel Motion Lid-Driven Cavity,” Journal of Mechanics, 31, pp.1-8 (2015).
27. Sorensen, D. C., “Implicit Application of Polynomial Filters in a k-Step Arnoldi Method,” SIAM Journal on Matrix Analysis and Applications, 13, pp. 357367 (1992).
28. Luo, W. J., “Transient Electroosmotic Flow Induced by dc or ac Electric Fields in a Curved Micro-Tube,” Journal of Colloid and Interface Science, 278, pp. 497507 (2004).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Mechanics
  • ISSN: 1727-7191
  • EISSN: 1811-8216
  • URL: /core/journals/journal-of-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed