Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-17T21:16:32.102Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent flow in wavy pipes

Published online by Cambridge University Press:  29 March 2006

Sheng-Tien Hsu  and
John F. Kennedy
Sheng-Tien Hsu
Affiliation:
Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa Present address: Tennessee Valley Authority Hydraulic Laboratory, Norris, Tennessee
John F. Kennedy
Affiliation:
Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa
Get access Rights & Permissions [Opens in a new window]

Abstract

A primarily experimental investigation was undertaken to determine the internal structure of steady, quasi-uniform, non-separated, axisymmetric flows in circular pipes with sinusoidal wall profiles. The quantities measured include radial and longitudinal distributions of mean velocity, pressure, and total head; the Reynolds shear stress and all three components of turbulence velocity; and boundary shear stress and pressure. Two different wall-wave steepnesses were investigated, and a constant Reynolds number of 1·13 × 105 (based on the average pipe diameter) was maintained in most experiments. The boundary shear stress was found to be shifted upstream relative to the boundary wave, whereas the wall pressure is shifted slightly downstream. The turbulence measurements revealed that there is a central core extending over some 60% of the pipe radius in which the turbulence quantities are constant along the pipe. Near the boundary, however, the turbulence velocities and stress vary periodically along the boundary waves. The longitudinal component of mean velocity was found to be distributed radially according to the power law, but with an exponent that varies along each wave; a simple analytical model is constructed to predict the variation of the exponent. It was not found possible to relate the local boundary shear stress to just the local flow characteristics, since the convective or ‘history’ effects play a significant role in its determination. An empirical formula is derived relating the local boundary shear stress to the local velocity distribution and the first two derivatives of the boundary profile.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 3 , 14 June 1971 , pp. 481 - 502
Copyright
© 1971 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. & Proudman, I. 1954 The effect of rapid distortion of a fluid in turbulent motion Quart. J. Mech. Appl. Math. 7, 83–103.Google Scholar
Benjamin, T. B. 1959 Shearing flow over a wavy boundary J. Fluid Mech. 6, 161–205.Google Scholar
Brown, K. C. & Joubert, P. N. 1969 The measurement of skin friction in turbulent boundary layer with adverse pressure gradients J. Fluid Mech. 35, 737–757.Google Scholar
Glover, J. R. 1967 Old gold model, type 4-2H hot-wire anemometer and type 2 meanproduct computer. IIHR Report 105. Inst of Hydr. Res., The University of Iowa, Iowa City, Iowa.Google Scholar
Harlow, F. H. & Romero, N. C. 1969 Turbulence distortion in a nonuniform tunnel. Los Alamos Scientific Laboratory Report, LA-4247.Google Scholar
Hsu, S. T. 1968 Turbulent flow in wavy pipes. Ph.D. Thesis, The University of Iowa, Iowa City, Iowa.
Iwasa, Y. & Kennedy, J. F. 1968 Free surface shear flow over a wavy bed. J. Hydr. Division, ASCE 94, HY2, 431–454.Google Scholar
Larras, J. & Claria, A. 1960 Wind tunnel research on relative wave and wind action L'’ouille Blanche, 6, 647–677.Google Scholar
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA T.R. 1174.Google Scholar
Motzfeld, H. 1937 Die turbulente strömung an welligen wander Z. angew. Math. Mech. 17, 193–212.Google Scholar
Nunner, W. 1956 Wärmeübergang und Druckabfall in rauhen Rohren. VDI-Forschungsheft, no. 455.Google Scholar
Rechenberg, I., Schwefel, H. P. & Bienert, P. 1967 Messung kleiner Wandschubspannunger bei turbulenten Grenzschichten in Ablösenähe, Hermann Föttinger Institute für Strömungstenchnik, T.U. Berlin.
Rhyming, I. L. 1963 Non-equilibrium flow inside a wavy cylinder J. Fluid. Mech. 17, 551–560.Google Scholar
Robillard, L. & Kennedy, J. F. 1967 Some experimental observations on free surface shear flow over a wavy boundary. Proc. 12th Congress of IAHR, Ft. Collins, Colorado.
Taylor, G. I. 1935 Turbulence in a contracting stream Z. angew. Math. Mech. 15, 91–96.Google Scholar
Vincenti, W. G. 1959 Non-equilibrium flow over a wavy wall J. Fluid Mech. 6, 481–496.Google Scholar