Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T08:19:06.562Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence structural changes for a three-dimensional turbulent boundary layer in a 30° bend

Published online by Cambridge University Press:  26 April 2006

Walter R. Schwarz  and
Peter Bradshaw
Walter R. Schwarz
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA94305, USA
Peter Bradshaw
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A three-dimensional turbulent boundary layer (3DTBL) was generated on the floor of a low-speed wind tunnel by the imposition of a cross-stream pressure gradient using a 30° bend in the horizontal plane. The surface streamlines were deflected by as much as 22° relative to the local tunnel centreline. Downstream of the bend, the 3DTBL gradually relaxed towards a 2DTBL; this was an impulse-and-recovery experiment which focused on the outer layer. Mean velocities were measured with a three-hole yawmeter and turbulence quantities, which included the Reynolds-stress tensor and the triple products, were measured with a cross-wire hot-wire anemometer. The experiment isolated the effects of crossflow from those of adverse streamwise pressure gradients, which may have clouded interpretations of previous 3DTBL experiments. In particular, the detailed developments of the cross-stream shear stress and of the stress/energy ratio become clearer. The shear-stress vector lagged behind the velocity-gradient vector as crossflow developed; however, the two vectors became more closely aligned downstream of the bend. Reductions in the stress/energy ratio implied that crossflow made shear-stress production less efficient. Another effect of three-dimensionality was a change of sign in the vertical transport of turbulent kinetic energy by turbulence, in the inner part of the boundary layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 272 , 10 August 1994 , pp. 183 - 210
Copyright
Copyright © Cambridge University Press 1994

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.)

Footnotes

†

Present address: Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA

References

Anderson, S. D. & Eaton, J. K. 1987 An experimental investigation of pressure driven three-dimensional boundary layers. Stanford University Thermosciences Div. Rep. MD-49.CrossRefGoogle Scholar
Anderson, S. D. & Eaton, J. K. 1989 Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers. J. Fluid Mech. 202, 263–294.Google Scholar
Bearman, P. W. 1971 Corrections for the effect of ambient temperature drift on hot-wire measurements in incompressible flow. DISA Rep. 11, May 1971, pp. 25–30.Google Scholar
Berg van den, B. 1990 Turbulence modelling: survey of activities in Belgium and the Netherlands, an appraisal of the status and a view on the prospects. NLR Tech. Publication 90184 L.Google Scholar
Bissonnettte, L. R. & Mellor, G. L. 1974 Experiments on the behaviour of an axisymmetric turbulent boundary layer with a sudden circumferential strain. J. Fluid Mech. 63, 369–413.Google Scholar
Bradshaw, P. 1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625–645.Google Scholar
Bradshaw, P. 1990 Progress in turbulence research. AIAA 90–1480, presented at AIAA 21st Fluid Dynamics Meeting, Seattle, Washington.Google Scholar
Bradshaw, P. & Pontikos, N. S. 1985 Measurements in the turbulent boundary layer on an ‘infinite’ swept wing. J. Fluid Mech. 159, 105–130.Google Scholar
Bradshaw, P. & Terrrel, M. G. 1969 The response of a turbulent boundary layer on an ‘infinite’ swept wing to the sudden removal of pressure gradient. NPL Aero Rep. 1305.Google Scholar
Bryer, D. W. & Pankhurst, R. C. 1971 Pressure-Probe Methods for Determining Wind Speed and Flow Direction. London: HMSO.Google Scholar
Coleman, G. N., Ferziger, J. H. & Spalart, P. R. 1990 A numerical study of the turbulent Ekman layer. J. Fluid Mech. 213, 313–348.Google Scholar
Dechow, R. & Felsch, K. O. 1977 Measurements of the mean velocity and of the Reynolds stress tensor in a three-dimensional turbulent boundary layer induced by a cylinder standing on a flat wall. In Proc. of Symp. on Turbulent Shear Flows, Vol. 1, April 18–20, 1977, University Park, Pennsylvania.Google Scholar
Degani, A.T., Smith, F. T. & Walker, J. D. A. 1992 The three-dimensional turbulent boundary layer near a plane of symmetry. J. Fluid Mech. 234, 329–360.Google Scholar
DeGrande, G. & Hirsch, C. 1978 Three-dimensional incompressible turbulent boundary layers. Free Univ. of Brussels Rep. VUB-STR-8.Google Scholar
Driver, D. M. & Hebbar, S. K. 1987 Experimental study of a three-dimensional, shear-driven, turbulent boundary layer. AIAA J. 25, 35–42.Google Scholar
Driver, D. M. & Johnston, J. P. 1990 Experimental study of a three-dimensional shear-driven turbulent boundary layer with streamwise adverse pressure gradient. NASA Tech. Mem. 102211.Google Scholar
East, L. F. & Sawyer, W. G. 1979 Measurements of the turbulence ahead of a 45° swept step using a double split-film probe. RAE Tech. Rep. 79136.Google Scholar
Eaton, J. K. 1991 Turbulence structure and heat transfer in three-dimensional boundary layers. 9th Symp. on Energy Engineering Sciences, Argonne National Laboratories.Google Scholar
Elsenaar, A. & Boelsma, S. H. 1974 Measurements of the Reynolds stress tensor in a three-dimensional turbulent boundary layer under infinite swept wing conditions. NLR TR 74095 U.Google Scholar
Fanneløp, T. K. & Krogstad, P. A. 1975 Three-dimensional turbulent boundary layers in external flows: a report on Euromech 60. J. Fluid Mech. 71, 815–826.Google Scholar
Fernholz, H. H. & Vagt, J. D. 1981 Turbulence measurements in an adverse pressure gradient three-dimensional turbulent boundary layer along a circular cylinder. J. Fluid Mech. 111, 233–269.Google Scholar
Flack, K. A. & Johnston, J. P. 1993 Near-wall investigation of three-dimensional turbulent boundary layers. Stanford University Thermosciences Div. Rep. MD-63.Google Scholar
Gruschwitz, E. 1935 Turbulente Reibungsschicten mit Sekundärströmungen. Ing.-Arch. 6, 355–365.Google Scholar
Hawthorne, W. R. 1951 Secondary circulation in fluid flow. Proc. R. Soc. Lond. A 206, 374–387.Google Scholar
Johnston, J. P. 1960 On the three-dimensional turbulent boundary layer generated by secondary flow. Trans. ASME D:, J. Basic Engng 82, 233–248.Google Scholar
Johnston, J. P. 1970 Measurements in a three-dimensional turbulent boundary layer induced by a swept, forward-facing step. J. Fluid Mech. 42, 823–844.Google Scholar
Johnston, J. P. 1976 Experimental studies in three-dimensional turbulent boundary layers. Stanford University Thermosciences Div. Rep. MD-34.Google Scholar
Kays, W. M. & Crawford, M. E. 1993 Convective Heat and Mass Transfer, 3rd Edn. McGraw-Hill.Google Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN 3178.Google Scholar
Lakshminarayana, B. 1986 Turbulence modelling for complex shear flows. AIAA J. 24, 1900–1917.Google Scholar
Launder, B. E. 1988 Turbulence modelling of three-dimensional shear flows. AGARD-CP-438.Google Scholar
Littell, H. S. & Eaton, J. K. 1991 An experimental investigation of the three-dimensional boundary layer on a rotating disk. Stanford University Thermosciences Div. Rep. MD-60.Google Scholar
Lohmann, R. P. 1978 The response of a developed turbulent boundary layer to local transverse surface motion. Trans. ASME I: J. Fluids Engng 98, 355–363.Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv.Appl.Mech. 18, 123–176.Google Scholar
Moin, P., Shih, T. H., Driver, D. & Mansour, N. M. 1990 Direct numerical simulation of a three-dimensional turbulent boundary layer. Phys. Fluids A 2, 1846–1853.Google Scholar
Müller, U. R. 1982 Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer. J. Fluid Mech. 119, 121–153.Google Scholar
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.Google Scholar
Ölçmen, S. & Simpson, R. L. 1992 Perspective: on the near-wall similarity of three-dimensional turbulent boundary layers. Trans. ASME I: J. Fluids Engng, 114, 487–495.Google Scholar
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185–208.Google Scholar
Pierce, F. J. & Duerson, S. H. 1975 Reynolds stress tensors in an end-wall three-dimensional channel boundary layer. Trans. ASME I, J. Fluids Engng, 96, 61–67.Google Scholar
Pierce, F. J. & Ezekewe, C. I. 1976 Measured uw stress gradients in a three-dimensional turbulent boundary layer. Trans. ASME I: J. Fluids Engng 98, 6768–770.Google Scholar
Pierce, F. J., McAllister, J. E. & Tennant, M.H. 1983 Near-wall similarity in a pressure-driven three-dimensional turbulent boundary layer. Trans. ASME I: J. Fluids Engng 105, 257–262.Google Scholar
Purtell, L. P. 1992 Turbulence in complex flows: a selected review. AIAA 92-0435, presented at 30th Aerospace Sciences Meeting, January 1992, Reno, Nevada.CrossRefGoogle Scholar
Schwarz, W. R. & Bradshaw, P. 1992 Three-dimensional turbulent boundary layer in a 30 degree bend: experiment and modelling. Stanford University Thermosciences Div. Rep. MD-61.Google Scholar
Schwarz, W. R. & Bradshaw, P. 1994 Term-by-term tests of stress-transport models in a three-dimensional boundary layer. Phys. Fluids 6, 986–998.Google Scholar
Sendstad, O. & Moin, P. 1991 On the mechanics of 3-D turbulent boundary layers. in Proc. 8th Turbulent Shear Flows Symp., Sept. 9–11, Munich, Germany.Google Scholar
Spalart, P. R. 1989 Theoretical and numerical study of a three-dimensional turbulent boundary layer. J. Fluid Mech. 205, 319–340.Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradient. J. Fluid Mech. 249, 337–372.Google Scholar
Squire, H. B. & Winter, K. G. 1951 The secondary flow in a cascade of airfoils in a nonuniform stream. J. Aero. Sci. 18, 271–277.Google Scholar
Young, A. D. & Maas, J. N. 1936 The behavior of a Pitot tube in a transverse total-pressure gradient. Aero. Res. Coun. R & M 1770.Google Scholar