Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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Effect of Aspect Ratio on the Similarity of Developing Laminar Flows in Rectangular Ducts

사각 단면 관 내부의 발달하는 층류 유동 유사성에 종횡비가 미치는 영향

  • 이공희 (포항공과대학교 기계공학과) ;
  • 백제현 (포항공과대학교 기계공학과)
  • Published : 2004.04.01
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Abstract

A numerical study was conducted to show the effect of aspect ratio on the analogy of the developing laminar flows between in orthogonally rotating straight duct and in a stationary curved duct of rectangular cross-section. In order. to clarify the similarity of two nows, dimensionless parameters (equation omitted) and Rossby Ro= $w_{m}$$\Omega$ $d_{h}$, in a rotating straight duct were used as a set corresponding to Dean number, (equation omitted), and curvature ratio, λ=R/ $d_{h}$, in a stationary curved duct. Four. different aspect ratios A=0.25, 0.5, 2 and 4 were considered. Under the condition that the magnitudes of Ro and λ were large enough to satisfy the 'asymptotic invariance property' and the aspect ratio was larger than 1, there were strong quantitative similarities between the two flows such as flow patterns, friction factors, and maximum axial velocity magnitudes fur the same values of $K_{LR}$ and $K_{LC}$ . On the other hand, as the aspect ratio decreased below 1 (A=0.25 and 0.5), the difference of the secondary flow intensity between these two flows was enhanced and therefore the analogy of two flows was not so evident as that of the larger aspect ratio (A=2 and 4). 4).nd 4).

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References

  1. Baura, S. N., 1954, 'Secondary Flow in a Rotating Straight Pipe,' Proc. Royal Society London, A 227, pp. 133-139 https://doi.org/10.1098/rspa.1954.0285
  2. Ito, H. and Nanbu, K., 1971, 'Flow in Rotating Straight Pipes of Circular Cross Section,' ASME J. Basic Engineering, Vol. 93, pp. 383-394 https://doi.org/10.1115/1.3425260
  3. Yang, W. J., Fann, S. and Kim, J. H., 1994, 'Heat and Fluid Flow Inside Rotating Channels,' Applied Mechanics Review, Vol. 47, pp. 367-396 https://doi.org/10.1115/1.3111084
  4. Dean, W. R., 1927, 'Note on the Motion of Fluid in a Curved Pipe,' Philosophical Magazine, Vol. 4, pp. 208-223 https://doi.org/10.1080/14786440708564324
  5. Soh, W. Y., 1988, 'Developing Fluid Flow in a Curved Duct of Square Cross-Section and Its Fully Developed Dual Solutions,' J. Fluid Mechanics, Vol. 188, pp. 337-361 https://doi.org/10.1017/S0022112088000758
  6. Berger, S. A., Tabolt, L. and Yao, L.-S., 1983, 'Flow in Curved Pipes,' Annual Review Fluid Mechanics, Vol. 15, pp. 461-512 https://doi.org/10.1146/annurev.fl.15.010183.002333
  7. Lee, G. H. and Baek, J. H., 2000, 'Study on the Similarity of Laminar Flows between in Orthogonally Rotating Square Duct and Stationary Curved Square Duct,' Trans. KSME(B), Vol. 24, No. 12, pp. 1683-1691
  8. Lee, G. H. and Baek, J. H., 2002, 'A Numerical Study of the Similarity of Fully Developed Laminar Flows in Orthogonally Rotating Rectangular Ducts and Stationary Curved Rectangular Ducts of Arbitrary Aspect Ratio,' Computational Mechanics, Vol. 29, pp. 183- 190 https://doi.org/10.1007/s00466-002-0332-0
  9. Trefethen, L. M., 1957, 'Flow in Rotating Radial Ducts,' General Electric Report, No.55GL350-A
  10. Ishigaki, H., 1994, 'Analogy between Laminar Flows in Curved Pipes and Orthogonally Rotating Pipes,' J. Fluid Mech., Vol. 268, pp. 133-145 https://doi.org/10.1017/S0022112094001291
  11. Ishigaki, H., 1999, 'Analogy between Developing Laminar Flows in Curved Pipes and Orthogonally Rotating Pipes,' JSME Int. J.(B), Vol. 42, pp. 197-205 https://doi.org/10.1299/jsmeb.42.197
  12. Lee, G. H. and Baek, J. H., 2001, 'A Numerical Study on the Similarity of the Developing Laminar Flows Between in Orthogonally Rotating Square Duct and Stationary Curved Square Duct,' J. Computational Fluids Engineering, Vol. 6, No. 1, pp. 21-30
  13. Ito, H., 1959, 'Friction Factors for Turbulent Flow in Curved Pipes,' J. Basic Engineering, Vol. 81, pp. 123-134
  14. Austin, L. R. and Seader, J. D., 1973, 'Fully Developed Viscous Flow in Coiled Circular Pipe s,' AIChE J., Vol. 19, pp. 85-93 https://doi.org/10.1002/aic.690190113
  15. Jen, T.-C. and Lavine, A. S., 1992, 'Laminar Heat Transfer and Fluid Flow in the Entrance Region of a Rotating Duct with Rectangular Cross Section: The Effect of Aspect Ratio,' J. Heat Transfer, Vol. 114, pp. 574-581 https://doi.org/10.1115/1.2911320