Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-29T06:00:47.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows

Published online by Cambridge University Press:  12 April 2006

Daniel P. Zilker ,
Gerald W. Cook  and
Thomas J. Hanratty
Daniel P. Zilker
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
Gerald W. Cook
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
Thomas J. Hanratty
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements of the shear-stress variation along and the velocity profiles above a solid wavy wall bounding a turbulent flow are presented for waves with height-to-length ratios of 2a/λ = 0·0312 and 0·05. These are compared with previous measurements of the wall shear stress reported by Thorsness (1975) and by Morrisroe (1970) for 2a/λ = 0·012. The investigation covered a range of conditions from those for which a linear behaviour is observed to those for which a separated flow is just being initiated.

Pressure measurements indicate a linear response in that the spatial variation is described quite well by a single harmonic with a wavelength equal to that of the surface. However, the variation of τw for waves with 2a/λ = 0·0312 and 0·05 can be more rapid on the leeward side of the wave. The degree of departure from a sinusoidal variation increases with increasing wave height and fluid velocity and, from the results reported in this paper, it is suggested that nonlinear behaviour will become evident when au*/v [ges ] 27.

Many aspects of the flow for all three waves are described by a solution of the linear momentum equations previously presented by Thorsness (1975) and by Thorsness & Hanratty (1977). These include the phase and amplitude of the pressure profile and the first harmonic of the shear-stress profile and the velocity field outside the viscous wall region.

These results suggest that up to separation the flow is approximated quite well by linear theory. Nonlinearities affect the flow only in a region very close to the wave surface and are manifested by the appearance of higher harmonics in the variation of τw.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 29 - 51
Copyright
© 1977 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

Beavers, G. S., Sparrow, E. M. & Lloyd, R. J. 1971 J. Basic Engng 93, 296.
Benjamin, T. B. 1959 J. Fluid Mech. 6, 161.
Bunco, P. H. & Sandborn, V. A. 1973 Proc. Symp. Turbulence in Liquids, Univ. Missouri - Rolla.
Bonchkovskaya, T. V. 1955 Akad. Nauk SSSR, Morskoi Gidrofiz. Inst. 6, 98.
Clark, J. A. 1968 Dept. Mech. Engng. Queen's Univ. Belfast Rep. no. 253.
Cook, G. W. 1970 Turbulent flow over solid wavy surfaces. Ph.D. thesis, Dept. Chemical Engineering, University of Illinois, Urbana.
Dimopoulos, H. & Hanratty, T. J. 1968 J. Fluid Mech. 33, 303.
Fortuna, G. & Hanratty, T. J. 1971 Int. J. Heat Mass Transfer 14, 1499.
Hanratty, T. J. 1967 Phys. Fluids Suppl. 10, 5126.
Helmholtz, H. 1868 Mber. preuss Akad. Wiss. 24, 215.
Hussain, A. K. M. F. & Reynolds, W. C. 1970 Thermosci. Div., Stanford Univ. Rep. FM-6.
Jolls, K. R. & Hanratty, T. J. 1969 A.I.Ch.E. J. 15, 199.
Kline, S. J., Morkovin, M. V. & Cockrell, D. J. 1969 Comp. Turbulent Boundary Layers: 1968 ASSOR - IFP - Stanford Conf. Thermosci. Div., Stanford Univ.
Larras, J. & Claria, A. 1960 Houille Blanche 6, 674.
Loyd, R. J., Moffat, R. J.& Kays, W. M. 1970 Thermosci. Div., Stanford Univ. Rep. HMT-13.
Mitchell, J. E. & Hanratty, T. J. 1966 J. Fluid Mech. 26, 199.
Morrisroe, P. E. 1970 Flow over solid wavy surfaces. M.S. thesis, Dept. Chemical Engineering, University of Illinois, Urbana.
Motzfield, H. 1937 Z. angew. Math. Mech. 17, 193.
Patel, V. C. & Head, M. R. 1969 J. Fluid Mech. 38, 181.
Saeger, J. C. & Reynolds, W. C. 1971 Thermosci. Div., Stanford Univ. Rep. FM-9.
Shaw, D. A. 1976 Mechanism of turbulent mass transfer to a pipe wall at high Schmidt numbers. Ph.D. thesis, Dept. Chemical Engineering, University of Illinois, Urbana.
Sigal, A. 1971 Ph.D. thesis, Dept. Aeronautical Engineering, California Institute of Technology.
Sirkar, K. K. & Hanratty, T. J. 1970 J. Fluid Mech. 44, 605.
Son, J. S. & Hanratty, T. J. 1969 J. Fluid Mech. 35, 353.
Thorsness, C. B. 1975 Transport phenomena associated with flow over a solid wavy surface. Ph.D. thesis, Dept. Chemical Engineering, University of Illinois, Urbana.
Thorsness, C. B. & Hanratty, T. J. 1977 Turbulent flow over wavy surfaces. In Proc. Symp. Turbulent Flows, Pennsylvania State Univ.
Zagustin, K., Hsu, E. Y., Street, R. L. & Perry, B. 1966 Dept. Civil Engng, Stanford Univ. Tech. Rep. no. 60.
Zilker, D. P. 1972 Flow over wavy surfaces. M.S. thesis. Dept. Chemical Engineering, University of Illinois, Urbana.
Zilker, D. P. 1976 Flow over wavy surfaces. Ph.D. thesis, Dept. Chemical Engineering, University of Illinois, Urbana.