A New Statistical-Based Correlation for the Rib Fin Effects on the Overall Heat Transfer Coefficient in a Rib-Roughened Cooling Channel

Taslim, M. E.; Nezym, V.

doi:https://doi.org/10.1155/2007/68684

International Journal of Rotating Machinery

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Research Article | Open Access

Volume 2007 | Article ID 068684 | https://doi.org/10.1155/2007/68684

A New Statistical-Based Correlation for the Rib Fin Effects on the Overall Heat Transfer Coefficient in a Rib-Roughened Cooling Channel

M. E. Taslim¹and V. Nezym²

Academic Editor: J. C. Han

Received08 Jan 2007

Accepted10 Jul 2007

Published22 Aug 2007

Abstract

Heat transfer coefficients in the cooling cavities of turbine airfoils are greatly enhanced by the presence of discrete ribs on the cavity walls. These ribs introduce two heat transfer enhancing features: a significant increase in heat transfer coefficient by promoting turbulence and mixing, and an increase in heat transfer area. Considerable amount of data are reported in open literature for the heat transfer coefficients both on the rib surface and on the floor area between the ribs. Many airfoil cooling design software tools, however, require an overall average heat transfer coefficient on a rib-roughened wall. Dealing with a complex flow circuit in conjunction with 180∘ bends, numerous film holes, trailing-edge slots, tip bleeds, crossover impingement, and a conjugate heat transfer problem; these tools are not often able to handle the geometric details of the rib-roughened surfaces or local variations in heat transfer coefficient on a rib-roughened wall. On the other hand, assigning an overall area-weighted average heat transfer coefficient based on the rib and floor area and their corresponding heat transfer coefficients will have the inherent error of assuming a 100% fin efficiency for the ribs, that is, assuming that rib surface temperature is the same as the rib base temperature. Depending on the rib geometry, this error could produce an overestimation of up to 10% in the evaluated rib-roughened wall heat transfer coefficient. In this paper, a correction factor is developed that can be applied to the overall area-weighted average heat transfer coefficient that, when applied to the projected rib-roughened cooling cavity walls, the net heat removal from the airfoil is the same as that of the rib-roughened wall. To develop this correction factor, the experimental results of heat transfer coefficients on the rib and on the surface area between the ribs are combined with about 400 numerical conduction models to determine an overall equivalent heat transfer coefficient that can be used in airfoil cooling design software. A well-known group method of data handling (GMDH) scheme was then utilized to develop a correlation that encompasses most pertinent parameters including the rib geometry, rib fin efficiency, and the rib and floor heat transfer coefficients.

References

N. Abuaf, R. Gibbs, and R. Baum, “Pressure drop and heat transfer coefficient distributions in serpentine passages with and without turbulence promoters,” in Proceedings of the 8th International Heat Transfer Conference, C. L. Tien, V. P. Carey, and J. K. Ferrell, Eds., vol. 6, pp. 2837–2845, San Francisco, Calif, USA, August 1986.
View at: Google Scholar
F. Burggraf, “Experimental heat transfer and pressure drop with two dimensional turbulence promoters applied to two opposite walls of a square tube,” in ASME, Augmentation of Convective Heat and Mass Transfer, A. E. Bergles and R. L. Webb, Eds., pp. 70–79, New York, NY, USA, 1970.
View at: Google Scholar
P. R. Chandra, J. C. Han, and S. C. Lau, “Effect of rib angle on local heat/mass transfer distribution in a two-pass rib-roughened channel,” in ASME, International Gas Turbine Conference and Exhibition, p. 9, Anaheim, Calif, USA, May-June 1987.
View at: Google Scholar
P. R. Chandra and J. C. Han, “Pressure drop and mass transfer in two-pass ribbed channels,” Journal of Thermophysics and Heat Transfer, vol. 3, no. 3, pp. 315–319, 1989.
View at: Google Scholar
J. C. Han, L. R. Glicksman, and W. M. Rohsenow, “An investigation of heat transfer and friction for rib-roughened surfaces,” International Journal of Heat and Mass Transfer, vol. 21, no. 8, pp. 1143–1156, 1978.
View at: Publisher Site | Google Scholar
J. C. Han, J. S. Park, and C. K. Lei, “Heat transfer enhancemenin channels with turbulence promoters,” Journal of Engineering for Gas Turbines and Power, vol. 107, pp. 628–635, 1985.
View at: Google Scholar
J. C. Han, Y. M. Zhang, and C. P. Lee, “Influence of surface heat flux ratio on heat transfer augmentation in square channels with parallel, crossed, and V-shaped angled ribs,” Journal of Turbomachinery, vol. 114, no. 4, pp. 872–880, 1992.
View at: Google Scholar
J. C. Han, “Heat transfer and friction in channels with two opposite rib-roughened walls,” Journal of Heat Transfer, vol. 106, no. 4, pp. 774–781, 1984.
View at: Google Scholar
T. M. Liou, J. J. Hwang, and S. H. Chen, “Turbulent heat transfer and fluid flow in a channel with repeated rib pairs,” in Proceedings of the ASME/JSME Thermal Engineering Joint Conference, vol. 3, pp. 205–212, Reno, Nev, USA, March 1991.
View at: Google Scholar
T.-M. Liou and J.-J. Hwang, “Effect of ridge shapes on turbulent heat transfer and friction in a rectangular channel,” International Journal of Heat and Mass Transfer, vol. 36, no. 4, pp. 931–940, 1993.
View at: Publisher Site | Google Scholar
D. E. Metzger, C. S. Fan, and J. W. Pennington, “Heat transfer and flow friction characteristics of very rough transverse ribbed surfaces with and without pin fins,” in Proceedings of the ASME/JSME Thermal Engineering Joint Conference, vol. 1, pp. 429–436, Honolulu, Hawaii, USA, March 1983.
View at: Google Scholar
D. E. Metzger, M. K. Chyu, and R. S. Bunker, “The contribution of on-rib heat transfer coefficients to total heat transfer from rib-roughened surfaces,” in Transport Phenomena in Rotating Machinery, J. H. Kim and W.-J. Yang, Eds., Hemisphere, Washington, DC, USA, 1988.
View at: Google Scholar
D. E. Metzger, C. S. Fan, and Y. Yu, “Effects of rib angle and orientation on local heat transfer in square channels with angled roughness ribs,” in Compact Heat Exchangers: A Festschrift for A.L. London, pp. 151–167, Hemisphere, Washington, DC, USA, 1990.
View at: Google Scholar
M. E. Taslim and S. D. Spring, “Experimental investigation of heat transfer coefficients and friction factors in passages of different aspect ratios roughened with $45^{\circ}$ turbulators,” in Proceedings of National Heat Transfer Conference, vol. 96, pp. 661–668, Houston, Tex, USA, July 1988.
View at: Google Scholar
M. E. Taslim and S. D. Spring, “Experimental heat transfer and friction factors in turbulated cooling passages of different aspect ratios, where turbulators are staggered,” in AIAA, ASME, SAE and ASEE Joint Propulsion Conference, p. 8, Boston, Mass, USA, July 1988.
View at: Google Scholar
M. E. Taslim and S. D. Spring, “Effects of turbulator profile and spacing on heat transfer and friction in a channel,” Journal of Thermophysics and Heat Transfer, vol. 8, no. 3, pp. 555–562, 1994.
View at: Google Scholar
M. E. Taslim, T. Li, and D. M. Kercher, “Experimental heat transfer and friction in channels roughened with angled, V-shaped, and discrete ribs on two opposite walls,” Journal of Turbomachinery, vol. 118, no. 1, pp. 20–28, 1996.
View at: Google Scholar
M. E. Taslim, T. Li, and S. D. Spring, “Measurements of heat transfer coefficients and friction factors in passages rib-roughened on all walls,” Journal of Turbomachinery, vol. 120, no. 3, pp. 564–570, 1998.
View at: Google Scholar
M. E. Taslim and C. M. Wadsworth, “An experimental investigation of the rib surface-averaged heat transfer coefficient in a rib-roughened square passage,” Journal of Turbomachinery, vol. 119, no. 2, pp. 381–389, 1997.
View at: Google Scholar
G. J. Korotky and M. E. Taslim, “Rib heat transfer coefficient measurements in a rib-roughened square passage,” Journal of Turbomachinery, vol. 120, no. 2, pp. 376–385, 1997.
View at: Google Scholar
M. E. Taslim and G. J. Korotky, “Low-aspect-ratio rib heat transfer coefficient measurements in a square channel,” Journal of Turbomachinery, vol. 120, no. 4, pp. 831–838, 1998.
View at: Google Scholar
M. E. Taslim and A. Lengkong, “ $45^{\circ}$ staggered rib heat transfer coefficient measurements in a square channel,” Journal of Turbomachinery, vol. 120, no. 3, pp. 571–580, 1998.
View at: Google Scholar
M. E. Taslim and A. Lengkong, “ $45^{\circ}$ round-corner rib heat transfer coefficient measurements in a square channel,” Journal of Turbomachinery, vol. 121, no. 2, pp. 272–280, 1999.
View at: Google Scholar
R. L. Webb, E. R. G. Eckert, and R. J. Goldstein, “Heat transfer and friction in tubes with repeated-rib roughness,” International Journal of Heat and Mass Transfer, vol. 14, no. 4, pp. 601–617, 1971.
View at: Publisher Site | Google Scholar
M. E. Taslim, “Rib fin effects on the overall equivalent heat transfer coefficient in a rib-roughened cooling channel,” International Journal of Heat Exchangers, vol. 6, no. 2, pp. 135–152, 2005.
View at: Google Scholar
A. G. Ivakhnenko, “Articles, papers, books and software on the Group Method of Data Handling (GMDH),” http://www.gmdh.net/articles/.
View at: Google Scholar
A. G. Ivakhnenko and Y. P. Yurachkovsky, Complicated Systems Modelling Using Empiric Data, Radio i Svyaz, Moscow, Russia, 1987.
View at: Google Scholar
V. Nezym, “Development of statistical model for casing treatment use,” International Journal of Turbo and Jet Engines, vol. 20, no. 4, pp. 267–274, 2003.
View at: Google Scholar
V. Nezym, J. Gomez-Mancilla, and S. V. Korkishko, “Statistical model for turning angle determination of compressor tandem cascade,” in Proceedings of the 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Hawaii, USA, March 2004.
View at: Google Scholar

Copyright

Copyright © 2007 M. E. Taslim and V. Nezym. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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