Flow transitions and combined free and forced convective heat transfer in rotating curved channels: The case of positive rotation

Physics of Fluids

Volumn 8, Issue 6, 1996, Pages 1553-1573

  Wang, Liqiu ^a   Cheng, K C ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

HEAT TRANSFER; HYDRODYNAMICS;

EID: 0029672414     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.868930     Document Type: Article

References (54)

1. W. D. Morris, Heat Transfer and Fluid Flow in Rotating Coolant Channels (Research Studies Press, Wiley, Chichester, 1981), pp. 27-31.
2. W. R. Dean, "The stream-line motion of a fluid in a curved pipe," Philos. Mag. 5, 673 (1928).
3. L. Wang, "Fluid flow and heat transfer in rotating curved channels, Ph.D. thesis, Department of Mechanical Engineering. University of Alberta, 1995.
4. 2. They play a similar role as that of the Dean number in the Dean problem for the mixed-convection problem and the Coriolis problem, respectively. Here we use D to denote this analogous role, and subscripts m and Ω to denote mixed-convection problem and Coriolis problem (effect of rotation Ω).
5. K. H. Winters, "A bifurcation study of laminar flow in a curved tube of rectangular cross-section," J. Fluid Mech. 180, 343 (1987).
6. K. Nandakumar, H. Raszillier, and F. Durst, "Flow through rotating rectangular ducts," Phys. Fluids A 3, 770 (1991).
7. K. Nandakumar and H. J. Weinitschke, " A bifurcation study of mixed-convection heat transfer in horizontal ducts," J. Fluid Mech. 231, 157 (1991).
8. S. R. Sankar, K. Nandakumar, and J. H. Masliyah, "Oscillatory flows in coiled square ducts," Phys. Fluids 31, 1348 (1988).
9. K. Nandakumar and J. H. Masliyah, "Swirling flow and heat transfer in coiled and twisted pipes," Adv. Transport Proc. 4, 49 (1986).
10. G. J. Hwang and C. H. Chao, "Forced laminar convection in a curved isothermal square duct," J. Heat Transfer 113, 48 (1991).
11. W. J. Yang, S. Fan, and J. H. Kim, "Heat and fluid flow inside rotating channels," Appl. Mech. Rev. 47, 367 (1994).
12. L. M. Hocking, "Boundary and shear layers in a curved rotating pipe," J. Math. Phys. Sci. 1, 123 (1967).
13. H. Ludwieg, "Die ausgebildete kanalströmung in einem rotierenden systern," Ing. Arch. Bd. 19, 296 (1951).
14. H. Ito and T. Motai, "Secondary flow in a rotating curved pipe," Rep. Inst. High Speed Mech. 29, 33 (1974).
15. H. Miyazaki, "Combined free and forced convective heat transfer and fluid flow in a rotating curved circular tube," Int. J. Heat Mass Transfer 14, 1295 (1971).
16. H. Miyazaki,"Combined free and forced convective heat transfer and fluid flow in a rotating curved rectangular tubes," J. Heat Transfer 95, 64 (1973).
17. S. Thangam and C. G. Speziale, "Numerical study of thermal convection in rotating channel flow," Int. J. Num. Methods Fluids 5, 133 (1985).
18. O. J. E. Matsson and P. H. Alfredsson, "The effect of spanwise system rotation on Dean vortices," J. Fluid Mech. 274, 243 (1994).
19. R. K. Shah and A. L. London, Laminar Flow Forced Convection in Ducts (Academic, New York, 1978).
20. S. W. Hong, S. M. Morcos, and A. E. Bergles, "Analytical and experimental results for combined forced and free convection in horizontal tubes," in Proceedings of the Fifth International Heat Transfer Conference, Vol. 3, p. 154 (1974).
21. E. R. G. Eckert and R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972), p. 525.
22. l which may be regarded as a modified rotation number.
23. L. Wang and K. C. Cheng, "Flow transition and combined free and forced convective heat transfer in a rotating curved circular tube," Int. J. Heat Mass Transfer (in press).
24. S. V. Patanker, Numerical Heat Transfer and Fluid Flow (Hemisphere, New York, 1980).
25. J. A. Baylis, "Experiments on laminar flow in curved channels of square section," J. Fluid Mech. 48, 417 (1971).
26. K. C. Cheng and M. Akiyama, "Laminar forced convection heat transfer in curved rectangular channels, " Int. J. Heat Mass Transfer 13, 471 (1970).
27. K. C. Cheng, R. C. Lin, and J. W. Ou, "Fully developed laminar flow in curved rectangular channels," J. Fluids Eng. 98, 41 (1976).
28. S. Thangam and N. Hur, "Laminar secondary flows in curved rectangular ducts," J. Fluid Mech 217, 421 (1990).
29. K. N. Ghia and J. S. Sokhey, "Laminar incompressible viscous flow in curved ducts of regular cross-sections," J. Fluids Eng. 99, 640 (1977).
30. Y. Mori, Y. Uchida, and T. Ukon, "Forced convective heat transfer in a curved channel with a square cross section," Int. J. Heat Mass Transfer 4, 1787 (1971).
31. K. C. Cheng, R. C. Lin, and J. W. Ou, "Graetz problem in curved square channels," J. Heat Transfer 97, 244 (1975).
32. Y. Mori and Y. Uchida, "Study on forced convective heat transfer in a curved square channel (1st report, theory of laminar region)," Trans. J. Soc. Mech. Eng. 33, 1836 (1967).
33. m Because of the change in friction resistance, it may vary even through the axial pressure gradient (also Dk) is fixed. Its variation at a fixed Dk is an indication of the change in friction resistance.
34. While the uniform grid spacing is used for all cases in the present work, the use of nonuniform mesh with appropriate distribution is desirable for the case of high rotation, strong curvature and heating/cooling in which a boundary layer appears near the wall and needs to be better resolved.
35. S. Yanase, N. Goto, and K. Yamamoto, "Stability of dual solutions of the flow in a curved circular tube," J. Phys. Soc. Jpn. 57, 2602 (1988).
36. E. M. Smirnov, "Asymptotic drag formulas for the rapidly rotating radial channels of rectangular cross section." Izv. Akad. Nauk. SSSR. Mekh. Zhidk. Gaza, 42 (1978).
37. C. G. Speziale, "Numerical study of viscous flow in rotating rectangular ducts," J. Fluid Mech. 122, 251 (1982).
38. W. H. Finlay, J. B. Keller, and J. H. Ferziger, "Instabilities and transition in curved channel flow," J. Fluid Mech. 194, 417 (1988).
39. W. H. Finaly, "Transition to oscillatory motion in rotating channel flow," J. Fluid Mech. 215, 209 (1990).
40. P. M. Ligrani, W. H. Finaly, W. A. Fields, S. T. Fuqua, and C. S. Subramaman, "Features of wavy vortices in a curved channel from experimental and numerical studies, " Phys. Fluids A 4, 695 (1992).
41. P. Ligrani and R. D. Niver, "Flow visualization of Dean vortices in a curved channel with 40 to 1 aspect ratio, " Phys. Fluids 31, 3605 (1988).
42. Y. Guo and W. H. Finlay, "Splittering, merging and wavelength selection of vortices in curved and/or rotating channel flow due to Eckhaus instability." J. Fluid Mech. 228, 661 (1991).
43. P. A. Alfredsson and H. Persson, "Instabilities in channel flow with system rotation," J. Fluid Mech. 202, 543 (1989).
44. O. J. E. Matsson and P. H. Alfredson, "Curvature- and rotation-induced instabilities in channel flow, " J. Fluid Mech. 210, 537 (1990).
45. D. J. Tritton and P. A. Davies, "Instabilities in geophysical dynamics," in Hydrodynamic Instabilities and the Transition to Turbulence, 2nd ed., edited by H. L. Swinney and J. P. Gollub (Springer-Verlag, Berlin, 1985), Vol. 45. p. 229.
46. L. Wang and K. C. Cheng, "Flow in curved channels with a low negative rotation speed," Phys. Rev. E 51, 1155 (1995).
47. L. wang and K. C. Cheng, "Visualization of flows in curved channels with a moderate or high rotation speed." Int. J. Rot. Mach. (in press).
48. M. D. Hoover and W. Stöber, "Model of particle deposition in spinning duct aerosol centrifuges," J. Aerosol Sci. 12, 223 (1981).
49. M. D. Hoover W. Stöber, and G. Morawietz, "Experiment on laminar flow in a rotating, curved duct of rectangular cross section," J. Fluid Eng. 106, 38 (1984).
50. I. Motabozi, C. Normand, H. Peerhossaini, and J. E. Westfreid, "Oscillatory modes in the flow betwee two horizontal corotating cylinders with a partially filled gap," Phys. Rev. A 39, 763 (1989).
51. O. J. E. Matsson, "Time-dependent instabilities in curved rotating channel flow," Phys. Fluids A 5, 1514 (1993).
52. B. Bara K. Nandakumar, and J. H. Masliyah, "An experimental and numerical study of the Dean problem: Flow development towards two-dimensional multiple solutions," J. Fluid Mech. 244, 339 (1992).
53. K. C. Cheng, J. Nakayama, and M. Akiyama, "Effect of finite and infinite aspect ratios on flow patterns in curved rectangular channels," in Flow Visualization, edited by T. Asanuma (Hemisphere, New York, 1979), pp. 181-186.
54. S. Sugiyama, T. Hayashi, and K. Yanazaki, "Flow characteristics in the curved rectangular channels (visualization of secondary flow)." Bull. J. Soc. Mech. Eng. 26, 964 (1983).