Bend Flow Calculational Methods Compared
Publication: Journal of Engineering Mechanics
Volume 110, Issue 11
Abstract
The two widely used methods of finite‐difference viscous‐flow calculation, the vorticity transport and primitive variable approaches, are applied to the analysis of flow through a plane short‐radius bend flanked by sections of straight conduit. Additionally, the vorticity transport method is employed in a direct (using combined rectangular and polar coordinates) and an indirect calculation (using a nonorthogonal coordinate transform). The solution for all three methods are found to be in essential agreement at a Reynolds number of 72. Because of the sharp curvature, the primitive variable method required pressure adjustment using a Poisson equation; velocities were adjusted by the divergence equation and advanced in time by the momentum equations. For the short‐radius bend, the matching procedures involved in the primitive variable approach were found to be crucial in developing smooth field transitions from one coordinate system to another. The adjustment of the coefficients in the transform vorticity transport method for the same regions (but not along the junction lines) were easily made and the comparisons with results from the other methods were excellent.
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References
1.
Clark, M. E., Robertson, J. M., and Cheng, L. C., “Interactive and Nonuniform Unsteady Physiological Flows by Finite Difference Transforms,” Proceedings of the Symposium on Computer Methods in Engineering, University of Southern California, Vol. 1, 1977, pp. 497–506.
2.
Dean, W. R., “The Streamline Motion of Flow in a Curved Pipe,” Philosophical Magazine, Vol. 4, 1927, p. 208,
also in Journal of Science, Vol. 5, 1928, p. 673.
3.
Dubuat, P. G. L., Principles D'hydraulique, Verifies Par Un Grand Nombre D'experiences Faites Par Ordre Du Government, nouv. ed., rev. et considerablement augm., 1786, p. 64.
4.
Fromm, J. E., “A Method for Computing Nonsteady Incompressible Viscous Fluid Flows,” Report No. LA‐2910, Los Alamos Scientific Laboratory, Los Alamos, N.M., 1963.
5.
Greenspan, D., “Secondary Flow in a Curved Tube,” Journal of Fluid Mechanics, Vol. 57, 1973, p. 167.
6.
Harlow, F. H., and Welch, J. E., “Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with a Free Surface,” Physics of Fluids, Vol. 8, No. 12, 1965, p. 2182.
7.
Hirt, C. W., Nichols, E. D., and Romero, N. C., “SOLA‐A Numerical Solution Algorithm for Transient Fluid Flows,” Report No. LA‐5852, Los Alamos Scientific Laboratory, Los Alamos, N.M., 1975.
8.
Huang, W. H., “Analysis of Two‐Dimensional 90‐Degree Bend Flow,” thesis presented to the University of Illinois, at Urbana, Ill., in 1966, (See ZAMP, Vol. 18, 1967, p. 621 and Proceedings, ASCE, Vol. 93, No. HY6, 1964) in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
9.
Humphrey, J. A. C., “Flow in Ducts with Curvature and Roughness,” thesis presented to the University of London, Imperial College, at London, England, in 1977, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
Hung, T. K., and Macagno, E. Q., “Laminar Eddies in a Two‐Dimensional Conduit Expansion,” La Houille Blanche, Vol. 21, No. 4, 1966, p. 391.
11.
Kawaguti, M., “Numerical Study of the Flow of a Viscous Fluid in a Curved Channel,” The Physics of Fluids, Vol. 12, supplement, 1969, p. 101.
12.
Liou, R. J., “Numerical Analysis of Two‐ and Three‐Dimensional 90‐Degree Bend Flow,” thesis presented to the University of Illinois, at Urbana‐Champaign, Ill., in 1980, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
13.
Liou, R. J., Clark, M. E., Robertson, J. M., and Cheng, L. C., “Precursor Numerical Studies of Aortic Arch Flow,” Proceedings of the 33rd Annual Conference on Engineering in Medicine and Biology, Vol. 22, 1980, p. 129.
14.
Liou, R. J., Clark, M. E., Robertson, J. M., and Cheng, L. C., “The Dynamics of Unsteady Bifurcation Flows,” Biofluid Mechanics, Vol. 2, 1980, p. 407.
15.
Oberkampf, W. L., and Goh, S. C., “Numerical Solutions of Incompressible Viscous Flow in Irregular Tubes,” Proceedings of International Conference on Computer Methods in Nonlinear Mechanics, J. T. Oden, ed., University of Texas, Austin, Tex., 1974, p. 569.
16.
Oberkampf, W. L., “Domain Mappings for the Numerical Solution of Partial Differential Equations,” International Journal for Numerical Methods in Engineering, Vol. 10, 1976, p. 211.
17.
Roache, P. J., Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, N.M., 1976, p. 202.
18.
Robertson, J. M., Clark, M. E., and Cheng, L. C., “Unsteady Flow Calculations for Acquisition of Steady Nonuniform Viscous Flows,” ASME, Symposium on Nonsteady Fluid Dynamics, 1978, p. 217.
19.
Robertson, J. M., Clark, M. E., and Cheng, L. C., “A Study of the Effects of a Transversely Moving Boundary on Plane Poiseuille Flow,” ASME, Journal of Biomechanical Engineering, Vol. 104, 1982, pp. 314–323.
20.
Thompson, J. F., Thames, F. C., and Mastin, C. W., “Automatic Numerical Generation of Body‐Fitted Curvilinear Coordinate System for a Field Containing Any Number of Arbitrary Two‐Dimensional Bodies,” Journal of Computational Physics, Vol. 15, 1974, p. 299
(See also Vol. 24, 1977, p. 245).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 110 • Issue 11 • November 1984
Pages: 1579 - 1596
Copyright
Copyright © 1984 ASCE.
History
Published online: Nov 1, 1984
Published in print: Nov 1984
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