TECHNICAL PAPERS
Mar 1, 1997

Supercritical Bend Flow

Publication: Journal of Hydraulic Engineering
Volume 123, Issue 3

Abstract

Supercritical flow in chute bends is considered both theoretically and experimentally. The conventional approach is found to apply to small relative curvature only. The knowledge is extended to large bend numbers, and a design procedure is presented. Supercritical bend flow in the smooth horizontal and rectangular channel is considered. It is found that the maximum standing wave heights are influenced by the bend number, that is, the approach Froude number times the square root of the average relative curvature. Current models are demonstrated to apply for relatively small bend numbers. For modest and large bend numbers, however, the flow pattern is modified. Besides the extreme wave lengths, the generalized surface profiles along either bend wall, the typical velocity fields, and the separation mechanism are experimentally studied. Also, a model for separated bend flow is developed. Photographs are presented that illustrate the uneven distribution of separated bend flow in regard to the cross-sectional area. This study allows a simple and straightforward design of chute bends.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Ellis, J., and Pender, G. (1982). “Chute spillway design calculations.”Proc., Inst. Civ. Engrs., 73(2), Thomas Telford Ltd., London, England, 299–312.
2.
Ellis, J.(1985a). “Numerical analysis of Kielder dam spillway.”J. Inst. Water Engrs., 39, 254–270.
3.
Ellis, J. (1985b). “Numerical modelling of spillway flows.”Proc., 2nd Int. Conf., The Hydraulics of Floods and Flood Control, B(1), 73–90.
4.
Hager, W. H. (1992). “Spillways: shockwaves and air entrainment.”International Commission on Large Dams (ICOLD) Bulletin 81. Commission Internationale des Grands Barrages, Paris, France.
5.
Hager, W. H., Schwalt, M., Jimenez, O., and Chaudhry, M. H.(1994). “Supercritical flow near an abrupt wall deflection.”J. Hydr. Res., Delft, The Netherlands, 32(1), 103–118.
6.
Ippen, A. T., and Knapp, R. T.(1936). “A study of high-velocity flow in curved channels of rectangular cross-section.”Trans. Am. Geophysical Union, 17, 516–521.
7.
Jobes, J. G., and Douma, J. H.(1942). “Testing theoretical losses in open channel flow. Part I: superelevation at bends.”Civ. Engrg., ASCE, 12(11), 613–615.
8.
Knapp, R. T.(1951). “Design of channel curves for supercritical flow.”Trans. ASCE, 116, 296–325.
9.
Knapp, R. T., and Ippen, A. T. (1938). “Curvilinear flow of liquids with free surfaces at velocities above that of wave propagation.”Proc., 5th Int. Congr. of Appl. Mech., Cambridge University Press, New York, N.Y., 531–536.
10.
Marchi, E. (1988). “Correnti veloci in curve a 90° molto strette.”Idrotecnica, Milan, Italy, 14(6), 439–455 (in Italian).
11.
Poggi, B. (1956). “Correnti veloci nei canali in curva.”L'Energia Elettrica, Milan, Italy, 33, 465–480 (in Italian).
12.
Rakotoarivelo, W., and Sananes, F. (1967). “Etude de l'écoulement supercritique dans un canal dont la section est en forme de U.”Proc., 12th Int. Assn. of Hydr. Res. Congr., 1(A38), 1–7 (in French).
13.
Sananes, F., and Acatay, T. (1962). “Contribution à l'étude des écoulements supercritiques dans des canaux coudés.”Comptes Rendus de l'Academie des Sciences, Paris, France, 255, 471–473 (in French).
14.
Schwalt, M., and Hager, W. H. (1993). “Ausmessen von Hochgeschwindigkeits-Strömungen.” (“Experimental observation of high velocity flows”). Wasser Energie Luft, Baden, Switzerland, 85(7/8), 157–162 (in German).
15.
Wilson, W. E.(1941). “Effects of curvature in supercritical flow.”Civ. Engrg., ASCE, 11(2), 94–95.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 123Issue 3March 1997
Pages: 208 - 218

History

Published online: Mar 1, 1997
Published in print: Mar 1997

Permissions

Request permissions for this article.

Authors

Affiliations

Roger Reinauer
Rapp Ingenieure; formerly, PhD Student, Swiss Fed. Inst. of Technol.
Willi H. Hager, Fellow, ASCE
Sr. Res. Engr., VAW, ETH-Zentrum, CH-8092 Zurich, Switzerland.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share