Study of Fully Developed Incompressible Flow in Curved Ducts, Using a Multi-Grid Technique

K. N. Ghia; U. Ghia; C. T. Shin

doi:10.1115/1.3242652

Journal of Fluids Engineering | Volume 109 | Issue 3 | Research Paper

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Study of Fully Developed Incompressible Flow in Curved Ducts, Using a Multi-Grid Technique

K. N. Ghia, U. Ghia and C. T. Shin

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K. N. Ghia, U. Ghia, C. T. Shin

Department of Aerospace Engineering and Applied Mechanics, University of Cincinnati, Cincinnati, Ohio 45221

J. Fluids Eng 109(3), 226-236 (Sep 01, 1987) (11 pages) doi:10.1115/1.3242652 History: Received July 23, 1982; Online October 26, 2009

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Abstract

Fully developed flows inside curved ducts of rectangular as well as polar cross sections have been analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow have been obtained using efficient numerical schemes. For curved-duct flows, the similarity parameter of significance is the Dean number K, rather than the Reynolds number Re. Results have been obtained for curved ducts with square cross sections for K up to 900 which, in the present study, corresponds to Re = 9,000 for this internal flow configuration. The fine-grid calculations show that, for square cross-section ducts, Dean’s instability occurs at K ≈ 125 and, further, that this phenomenon does not disappear even for K = 900. In ducts of polar cross sections, which are geometrically more representative of turbomachinery cascade passages, the phenomenon of Dean’s instability is not seen to occur for K up to 600.

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Ghia KN, Ghia UU, Shin CT. Study of Fully Developed Incompressible Flow in Curved Ducts, Using a Multi-Grid Technique. ASME. J. Fluids Eng. 1987;109(3):226-236. doi:10.1115/1.3242652.

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Study of Fully Developed Incompressible Flow in Curved Ducts, Using a Multi-Grid Technique

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