Combined Effects of Centrifugal and Coriolis Instability of the Flow through a Rotating Curved Duct with Rectangular Cross Section

Abstract

Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of the Taylor number  for a constant Dean number. The rotation of the duct about the center of curvature is imposed in the positive direction, and the effects of rotation (Coriolis force) on the flow characteristics are investigated. As a result, multiple branches of asymmetric steady solutions with two-, three-and multi-vortex solutions are obtained. To investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the unsteady solutions are performed, and it is found that the unsteady flow undergoes through various flow instabilities in the scenario “chaotic → multi-periodic → periodic → steady-state”, if Tr is increased in the positive direction. The present results show the characteristics of both the secondary flow and axial flow distribution in the flow.

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Mondal, R. , Ray, S. and Yanase, S. (2014) Combined Effects of Centrifugal and Coriolis Instability of the Flow through a Rotating Curved Duct with Rectangular Cross Section. Open Journal of Fluid Dynamics, 4, 1-14. doi: 10.4236/ojfd.2014.41001.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Ishigaki, H. (1993) Fundamental Characteristics of Laminar Flows in a Rotating Curved Pipe. Transactions of JSME, 59, 1494-1501.
[2] Ishigaki, H. (1996) Laminar Flow in Rotating Curved Pipes. Journal of Fluid Mechanics, 329, 373-388. http://dx.doi.org/10.1017/S0022112096008956
[3] Berger, S.A., Talbot, L. and Yao, L.S. (1983) Flow in Curved Pipes. Annual Review of Fluid Mechanics, 35, 461-512. http://dx.doi.org/10.1146/annurev.fl.15.010183.002333
[4] Nandakumar, K. and Masliyah, J.H. (1986) Swirling Flow and Heat Transfer in Coiled and Twisted Pipes. Advanced Transport Processes, 4, 49-112.
[5] Winters, K.H. (1987) A Bifurcation Study of Laminar Flow in a Curved Tube of Rectangular Cross-Section. Journal of Fluid Mechanics, 180, 343-369. http://dx.doi.org/10.1017/S0022112087001848
[6] Mondal, R.N., Kaga, Y., Hyakutake, T. and Yanase, S. (2007) Bifurcation Diagram for Two-Dimensional Steady Flow and Unsteady Solutions in a Curved Square Duct. Fluid Dynamics Research, 39, 413-446. http://dx.doi.org/10.1016/j.fluiddyn.2006.10.001
[7] Selmi, M., Namdakumar, K. and Finlay, W.H. (1994) A Bifurcation Study of Viscous Flow through a Rotating Curved Duct. Journal of Fluid Mechanics, 262, 353-375. http://dx.doi.org/10.1017/S0022112094000534
[8] Selmi, M. and Namdakumar, K. (1999) Bifurcation Study of the Flow through Rotating Curved Ducts. Physics of Fluids, 11, 2030-2043. http://dx.doi.org/10.1063/1.870066
[9] Yamamoto, K., Yanase, S. and Alam, M.M. (1999) Flow through a Rotating Curved Duct with Square Cross-Section. Journal of the Physical Society of Japan, 68, 1173-1184. http://dx.doi.org/10.1143/JPSJ.68.1173
[10] Mondal, R.N., Islam, M.R., Uddin, M.S. and Datta, A.K. (2010) Flow through a Rotating Curved Square Duct: The Case of Positive Rotation. Journal of Physical Science, 14, 145-163.
[11] Wang, L.Q. and Cheng, K.C. (1996) Flow Transitions and Combined Free and Forced Convective Heat Transfer in Rotating Curved Channels: The Case of Positive Rotation. Physics of Fluids, 8, 1553-1573. http://dx.doi.org/10.1063/1.868930
[12] Zhang, J.S., Zhang, B.Z. and Jü, J. (2001) Fluid Flow in a Rotating Curved Rectangular Duct. International Journal of Heat and Fluid Flow, 22, 583-592. http://dx.doi.org/10.1016/S0142-727X(01)00126-6
[13] Mondal, R.N., Alam, M.M. and Yanase, S. (2007) Numerical Prediction of Non-Isothermal Flows through a Rotating Curved Duct with Square Cross Section. Thammasat International Journal of Science and Technology, 12, 24-43.
[14] Mondal, R.N., Datta, A.K. and Mondal, B. (2011) Bifurcation Study of Thermal Flows through a Rotating Curved Square Duct. Bangladesh Journal of Scientific and Industrial Research, 48, 59-70.
[15] Yamamoto, K., Wu, X., Nozaki, K. and Hayamizu, Y. (2006) Visualization of Taylor-Dean Flow in a Curved Duct of Square Cross-Section. Fluid Dynamics Research, 38, 1-18. http://dx.doi.org/10.1016/j.fluiddyn.2005.09.002
[16] Nobari, M.R.H., Nousha, A. and Damangir, E. (2009) A Numerical Investigation of Flow and Heat Transfer in Rotating U-Shaped Square Ducts. International Journal of Thermal Sciences, 48, 590-601. http://dx.doi.org/10.1016/j.ijthermalsci.2008.04.001
[17] Yanase, S. and Nishiyama, K. (1988) On the Bifurcation of Laminar Flows through a Curved Rectangular Tube. Journal of the Physical Society of Japan, 57, 3790-3795. http://dx.doi.org/10.1143/JPSJ.57.3790
[18] Yanase, S., Kaga, Y. and Daikai, R. (2002) Laminar Flow through a Curved Rectangular Duct over a Wide Range of the Aspect Ratio. Fluid Dynamics Research, 31, 151-183. http://dx.doi.org/10.1016/S0169-5983(02)00103-X
[19] Yang, T. and Wang, L. (2003) Bifurcation and Stability of Forced Convection in Rotating Curved Ducts of Square Cross Section. International Journal of Heat and Mass Transfer, 46, 613-629. http://dx.doi.org/10.1016/S0017-9310(02)00329-0
[20] Wang, L.Q. and Yang, T.L. (2004) Multiplicity and Stability of Convection in Curved Ducts: Review and Progress. Advances in Heat Transfer, 38, 203-256. http://dx.doi.org/10.1016/S0065-2717(04)38004-4
[21] Yanase, S., Mondal, R.N. and Kaga, Y. (2005) Numerical Study of Non-Isothermal Flow with Convective Heat Transfer in a Curved Rectangular Duct. International Journal of Thermal Sciences, 44, 1047-1060. http://dx.doi.org/10.1016/j.ijthermalsci.2005.03.013
[22] Mondal, R.N., Kaga, Y., Hyakutake, T. and Yanase, S. (2006) Effects of Curvature and Convective Heat Transfer in Curved Square Duct Flows. Journal of Fluids Engineering, ASME Journals, 128, 1013-1023. http://dx.doi.org/10.1115/1.2236131
[23] Gottlieb, D. and Orazag, S.A. (1977) Numerical Analysis of Spectral Methods. Society for Industrial and Applied Mathematics, Philadelphia. http://dx.doi.org/10.1137/1.9781611970425
[24] Keller, H.B. (1987) Lectures on Numerical Methods in Bifurcation Problems. Springer, Berlin.
[25] Mondal, R.N. (2006) Isothermal and Non-Isothermal Flows through Curved Duct with Square and Rectangular Cross-Section. Ph.D. Thesis, Okayama University, Okayama.

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