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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Druckformat: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v37.i1.60
pages 85-99

Numerical Prediction of Non-Isothermal Flow Through a Curved Square Duct

Rabindra Nath Mondal
Department of Mathematics, Jagannath University, Dhaka, Bangladesh
Md. Sharif Uddin
Mathematics Discipline; Science, Engineering and Technology School, Khulna University, Khulna-9208, Bangladesh
Shinichiro Yanase
Department of Mechanical Engineering, Faculty of Engineering, Okayama University Okayama 700-8530, Japan

ABSTRAKT

A numerical study is presented for the solution structure, stability and transitions of non-isothermal flow through a curved square duct by using a spectral method and covering a wide range of the Dean number, Dn, 0 ≤ Dn ≤ 6000 and the curvature, δ, 0 < δ ≤ 0.5. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 500, where the outer wall is heated and the inner one cooled. First, steady solutions are obtained by the Newton-Raphson iteration method. As a result, two branches of asymmetric steady solutions are obtained. Linear stability of the steady solutions is then investigated. It is found that only the first branch is linearly stable in a couple of interval of Dn for small δ; for large δ, however, the same branch is linearly stable in a single but wide interval of Dn though the branching pattern of the bifurcation diagram is unchanged. When there is no stable steady solution, time evolution calculations as well as their spectral analysis show that typical transition occurs from steady flow to chaos through various flow instabilities, if Dn is increased. It is also found that the transition to periodic or the chaotic state is delayed if the curvature is increased.

REFERENZEN

  1. Berger, S. A., Talbot, L., and Yao, L. S., Flow in Curved Pipes.

  2. Chandratilleke, T. T. and Nursubyakto, Numerical Prediction of Secondary Flow and Convective Heat Transfer in Externally Heated Curved Rectangular Ducts.

  3. Finlay, W. H. and Nandakumar, K., Onset of Two-Dimensional Cellular Flow in Finite Curved Channels of Large Aspect Ratio.

  4. Ito, H., Flow in Curved Pipes.

  5. Ligrani, P. M. and Niver, R. D., Flow Visualization of Dean Vortices in a Curved Channel with 40 to 1 Aspect Ratio.

  6. 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.

  7. Mondal, R. N., Kaga, Y., Hyakutake, T., and Yanase, S., Effects of Curvature and Convective Heat Transfer in Curved Square Duct Flows.

  8. Mondal, R. N., Isothermal and Non-Isothermal Flows Through Curved Ducts with Square and Rectangular Cross Sections.

  9. Nandakumar, K. and Masliyah, J. H., Swirling Flow and Heat Transfer in Coiled and Twisted Pipes.

  10. Ruelle, D. and Takens, F., On the Nature of Turbulence.

  11. Wang, L. and Yang, T., Bifurcation and Stability of Forced Convection in Curved Square Ducts.

  12. Wang, L. and Yang, T., Periodic Oscillation in Curved Duct Flows.

  13. Winters, K. H., A Bifurcation Study of Laminar Flow in a Curved Tube of Rectangular Cross-Section.

  14. Yanase, S. Kaga, Y., and Daikai, R., Laminar Flows Through a Curved Rectangular Duct over a Wide Range of the Aspect Ratio.

  15. Yanase, S., Mondal, R. N., Kaga, Y., and Yamamoto, K., Transition from Steady to Chaotic States of Isothermal and Non-Isothermal Flows Through a Curved Rectangular Duct.


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